Sr Examen

Otras calculadoras

Simplificación de expresiones/ Descomposición en fracciones simples/ sin40/(2*cos20)

¿Cómo vas a descomponer esta sin40/(2*cos20) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
 sin(40) 
---------
2*cos(20)
sin⁡(40)2cos⁡(20)\frac{\sin{\left(40 \right)}}{2 \cos{\left(20 \right)}} 
sin(40)/((2*cos(20)))
Simplificación general [src] 
sin(20)
sin⁡(20)\sin{\left(20 \right)} 
sin(20)
Respuesta numérica [src] 
0.912945250727628
0.912945250727628
Potencias [src] 
   /   -40*I    40*I\ 
-I*\- e      + e    / 
----------------------
    / -20*I    20*I\  
  2*\e      + e    /
−i(e40i−e−40i)2(e−20i+e20i)- \frac{i \left(e^{40 i} - e^{- 40 i}\right)}{2 \left(e^{- 20 i} + e^{20 i}\right)} 
-i*(-exp(-40*i) + exp(40*i))/(2*(exp(-20*i) + exp(20*i)))
Abrimos la expresión [src] 
                                                                                             27                                                                                                                                                                                 31                                                                                                                                                                                 23                                                                                                                                                                                 35                                                                                                                                                                                19                                                                                                                                                                                 15                                                                                                                                                                                 39                                                                                                                                                                                11                                                                                                                                                                                7                                                                                                                                                                                3                                                                                                                                                                                                                                                                                                                                                                      5                                                                                                                                                                                    9                                                                                                                                                                                  13                                                                                                                                                                                  17                                                                                                                                                                                 37                                                                                                                                                                                  21                                                                                                                                                                                 33                                                                                                                                                                                 25                                                                                                                                                                                 29                                                                                   
                                                                           74327630282752*sin  (1)*cos(1)                                                                                                                                                     56221121904640*sin  (1)*cos(1)                                                                                                                                                     33087710822400*sin  (1)*cos(1)                                                                                                                                                     11441792876544*sin  (1)*cos(1)                                                                                                                                                     5250746941440*sin  (1)*cos(1)                                                                                                                                                       284817162240*sin  (1)*cos(1)                                                                                                                                                       274877906944*sin  (1)*cos(1)                                                                                                                                                        4564377600*sin  (1)*cos(1)                                                                                                                                                          15690048*sin (1)*cos(1)                                                                                                                                                              5320*sin (1)*cos(1)                                                                                                                                                                  20*cos(1)*sin(1)                                                                                                                                                                421344*sin (1)*cos(1)                                                                                                                                                             334721024*sin (1)*cos(1)                                                                                                                                                         42600857600*sin  (1)*cos(1)                                                                                                                                                       1407331860480*sin  (1)*cos(1)                                                                                                                                                      2611340115968*sin  (1)*cos(1)                                                                                                                                                      15002134118400*sin  (1)*cos(1)                                                                                                                                                     30666066493440*sin  (1)*cos(1)                                                                                                                                                     56469693136896*sin  (1)*cos(1)                                                                                                                                                     74693776244736*sin  (1)*cos(1)                                                                         
- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                 14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16                     14                 18                 10               6             2              4                20                8                 12                 16   
  1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)   1 - 6553600*cos  (1) - 2621440*cos  (1) - 2050048*cos  (1) - 84480*cos (1) - 200*cos (1) + 6600*cos (1) + 524288*cos  (1) + 549120*cos (1) + 4659200*cos  (1) + 5570560*cos  (1)
−74327630282752sin⁡27(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−33087710822400sin⁡23(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−56221121904640sin⁡31(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−5250746941440sin⁡19(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−11441792876544sin⁡35(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−284817162240sin⁡15(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−4564377600sin⁡11(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−274877906944sin⁡39(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−15690048sin⁡7(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)−5320sin⁡3(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+20sin⁡(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+421344sin⁡5(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+334721024sin⁡9(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+2611340115968sin⁡37(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+42600857600sin⁡13(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+1407331860480sin⁡17(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+30666066493440sin⁡33(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+15002134118400sin⁡21(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+74693776244736sin⁡29(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)+56469693136896sin⁡25(1)cos⁡(1)−2050048cos⁡10(1)−84480cos⁡6(1)−6553600cos⁡14(1)−200cos⁡2(1)−2621440cos⁡18(1)+1+524288cos⁡20(1)+5570560cos⁡16(1)+6600cos⁡4(1)+4659200cos⁡12(1)+549120cos⁡8(1)- \frac{74327630282752 \sin^{27}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{33087710822400 \sin^{23}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{56221121904640 \sin^{31}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{5250746941440 \sin^{19}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{11441792876544 \sin^{35}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{284817162240 \sin^{15}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{4564377600 \sin^{11}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{274877906944 \sin^{39}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{15690048 \sin^{7}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} - \frac{5320 \sin^{3}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{20 \sin{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{421344 \sin^{5}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{334721024 \sin^{9}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{2611340115968 \sin^{37}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{42600857600 \sin^{13}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{1407331860480 \sin^{17}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{30666066493440 \sin^{33}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{15002134118400 \sin^{21}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{74693776244736 \sin^{29}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} + \frac{56469693136896 \sin^{25}{\left(1 \right)} \cos{\left(1 \right)}}{- 2050048 \cos^{10}{\left(1 \right)} - 84480 \cos^{6}{\left(1 \right)} - 6553600 \cos^{14}{\left(1 \right)} - 200 \cos^{2}{\left(1 \right)} - 2621440 \cos^{18}{\left(1 \right)} + 1 + 524288 \cos^{20}{\left(1 \right)} + 5570560 \cos^{16}{\left(1 \right)} + 6600 \cos^{4}{\left(1 \right)} + 4659200 \cos^{12}{\left(1 \right)} + 549120 \cos^{8}{\left(1 \right)}} 
-74327630282752*sin(1)^27*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 56221121904640*sin(1)^31*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 33087710822400*sin(1)^23*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 11441792876544*sin(1)^35*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 5250746941440*sin(1)^19*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 284817162240*sin(1)^15*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 274877906944*sin(1)^39*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 4564377600*sin(1)^11*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 15690048*sin(1)^7*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) - 5320*sin(1)^3*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 20*cos(1)*sin(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 421344*sin(1)^5*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 334721024*sin(1)^9*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 42600857600*sin(1)^13*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 1407331860480*sin(1)^17*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 2611340115968*sin(1)^37*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 15002134118400*sin(1)^21*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 30666066493440*sin(1)^33*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 56469693136896*sin(1)^25*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16) + 74693776244736*sin(1)^29*cos(1)/(1 - 6553600*cos(1)^14 - 2621440*cos(1)^18 - 2050048*cos(1)^10 - 84480*cos(1)^6 - 200*cos(1)^2 + 6600*cos(1)^4 + 524288*cos(1)^20 + 549120*cos(1)^8 + 4659200*cos(1)^12 + 5570560*cos(1)^16)
Parte trigonométrica [src] 
sin(20)
sin⁡(20)\sin{\left(20 \right)} 
   /     pi\
cos|20 - --|
   \     2 /
cos⁡(20−π2)\cos{\left(20 - \frac{\pi}{2} \right)} 
   /     pi\
cos|40 - --|
   \     2 /
------------
 2*cos(20)
cos⁡(40−π2)2cos⁡(20)\frac{\cos{\left(40 - \frac{\pi}{2} \right)}}{2 \cos{\left(20 \right)}} 
 2*cot(10)  
------------
       2    
1 + cot (10)
2cot⁡(10)1+cot⁡2(10)\frac{2 \cot{\left(10 \right)}}{1 + \cot^{2}{\left(10 \right)}} 
   sec(20)    
--------------
     /     pi\
2*sec|40 - --|
     \     2 /
sec⁡(20)2sec⁡(40−π2)\frac{\sec{\left(20 \right)}}{2 \sec{\left(40 - \frac{\pi}{2} \right)}} 
                    1                
             1 + --------            
                    2                
                 cot (10)            
-------------------------------------
/       1    \ /       1    \        
|1 + --------|*|1 - --------|*cot(20)
|       2    | |       2    |        
\    cot (20)/ \    cot (10)/
1cot⁡2(10)+1(1−1cot⁡2(10))(1+1cot⁡2(20))cot⁡(20)\frac{\frac{1}{\cot^{2}{\left(10 \right)}} + 1}{\left(1 - \frac{1}{\cot^{2}{\left(10 \right)}}\right) \left(1 + \frac{1}{\cot^{2}{\left(20 \right)}}\right) \cot{\left(20 \right)}} 
/       2    \                
\1 + tan (10)/*sec(20)*sin(20)
------------------------------
/       2    \ /       2    \ 
\1 + tan (20)/*\1 - tan (10)/
(tan⁡2(10)+1)sin⁡(20)sec⁡(20)(1−tan⁡2(10))(1+tan⁡2(20))\frac{\left(\tan^{2}{\left(10 \right)} + 1\right) \sin{\left(20 \right)} \sec{\left(20 \right)}}{\left(1 - \tan^{2}{\left(10 \right)}\right) \left(1 + \tan^{2}{\left(20 \right)}\right)} 
     1      
------------
   /     pi\
sec|20 - --|
   \     2 /
1sec⁡(20−π2)\frac{1}{\sec{\left(20 - \frac{\pi}{2} \right)}} 
            /          2      \                     
            |       sec (10)  |                     
            |1 + -------------|*sec(20)             
            |       2/     pi\|                     
            |    sec |10 - --||                     
            \        \     2 //                     
----------------------------------------------------
/          2      \ /          2      \             
|       sec (20)  | |       sec (10)  |    /     pi\
|1 + -------------|*|1 - -------------|*sec|20 - --|
|       2/     pi\| |       2/     pi\|    \     2 /
|    sec |20 - --|| |    sec |10 - --||             
\        \     2 // \        \     2 //
(sec⁡2(10)sec⁡2(10−π2)+1)sec⁡(20)(1+sec⁡2(20)sec⁡2(20−π2))(−sec⁡2(10)sec⁡2(10−π2)+1)sec⁡(20−π2)\frac{\left(\frac{\sec^{2}{\left(10 \right)}}{\sec^{2}{\left(10 - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(20 \right)}}{\left(1 + \frac{\sec^{2}{\left(20 \right)}}{\sec^{2}{\left(20 - \frac{\pi}{2} \right)}}\right) \left(- \frac{\sec^{2}{\left(10 \right)}}{\sec^{2}{\left(10 - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(20 - \frac{\pi}{2} \right)}} 
 2*tan(10)  
------------
       2    
1 + tan (10)
2tan⁡(10)tan⁡2(10)+1\frac{2 \tan{\left(10 \right)}}{\tan^{2}{\left(10 \right)} + 1} 
        /       2    \               
        \1 + tan (10)/*sin(20)       
-------------------------------------
/       2    \ /       2    \        
\1 + tan (20)/*\1 - tan (10)/*cos(20)
(tan⁡2(10)+1)sin⁡(20)(1−tan⁡2(10))(1+tan⁡2(20))cos⁡(20)\frac{\left(\tan^{2}{\left(10 \right)} + 1\right) \sin{\left(20 \right)}}{\left(1 - \tan^{2}{\left(10 \right)}\right) \left(1 + \tan^{2}{\left(20 \right)}\right) \cos{\left(20 \right)}} 
   /      pi\
csc|-20 + --|
   \      2 /
-------------
  2*csc(40)
csc⁡(−20+π2)2csc⁡(40)\frac{\csc{\left(-20 + \frac{\pi}{2} \right)}}{2 \csc{\left(40 \right)}} 
   sin(40)    
--------------
     /     pi\
2*sin|20 + --|
     \     2 /
sin⁡(40)2sin⁡(π2+20)\frac{\sin{\left(40 \right)}}{2 \sin{\left(\frac{\pi}{2} + 20 \right)}} 
   1   
-------
csc(20)
1csc⁡(20)\frac{1}{\csc{\left(20 \right)}} 
                  /         4    \       
            2     |    4*sin (10)|       
       2*sin (20)*|1 + ----------|       
                  |        2     |       
                  \     sin (20) /       
-----------------------------------------
/         4    \ /         4    \        
|    4*sin (10)| |    4*sin (20)|        
|1 - ----------|*|1 + ----------|*sin(40)
|        2     | |        2     |        
\     sin (20) / \     sin (40) /
2(4sin⁡4(10)sin⁡2(20)+1)sin⁡2(20)(1+4sin⁡4(20)sin⁡2(40))(−4sin⁡4(10)sin⁡2(20)+1)sin⁡(40)\frac{2 \left(\frac{4 \sin^{4}{\left(10 \right)}}{\sin^{2}{\left(20 \right)}} + 1\right) \sin^{2}{\left(20 \right)}}{\left(1 + \frac{4 \sin^{4}{\left(20 \right)}}{\sin^{2}{\left(40 \right)}}\right) \left(- \frac{4 \sin^{4}{\left(10 \right)}}{\sin^{2}{\left(20 \right)}} + 1\right) \sin{\left(40 \right)}} 
 sec(20) 
---------
2*csc(40)
sec⁡(20)2csc⁡(40)\frac{\sec{\left(20 \right)}}{2 \csc{\left(40 \right)}} 
        /       2/      pi\\                     
        |    csc |-10 + --||                     
        |        \      2 /|    /      pi\       
        |1 + --------------|*csc|-20 + --|       
        |          2       |    \      2 /       
        \       csc (10)   /                     
-------------------------------------------------
/       2/      pi\\ /       2/      pi\\        
|    csc |-20 + --|| |    csc |-10 + --||        
|        \      2 /| |        \      2 /|        
|1 + --------------|*|1 - --------------|*csc(20)
|          2       | |          2       |        
\       csc (20)   / \       csc (10)   /
(csc⁡2(−10+π2)csc⁡2(10)+1)csc⁡(−20+π2)(1+csc⁡2(−20+π2)csc⁡2(20))(−csc⁡2(−10+π2)csc⁡2(10)+1)csc⁡(20)\frac{\left(\frac{\csc^{2}{\left(-10 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(10 \right)}} + 1\right) \csc{\left(-20 + \frac{\pi}{2} \right)}}{\left(1 + \frac{\csc^{2}{\left(-20 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(20 \right)}}\right) \left(- \frac{\csc^{2}{\left(-10 + \frac{\pi}{2} \right)}}{\csc^{2}{\left(10 \right)}} + 1\right) \csc{\left(20 \right)}} 
        /       2/     pi\\                    
        |    cos |10 - --||                    
        |        \     2 /|    /     pi\       
        |1 + -------------|*cos|20 - --|       
        |          2      |    \     2 /       
        \       cos (10)  /                    
-----------------------------------------------
/       2/     pi\\ /       2/     pi\\        
|    cos |20 - --|| |    cos |10 - --||        
|        \     2 /| |        \     2 /|        
|1 + -------------|*|1 - -------------|*cos(20)
|          2      | |          2      |        
\       cos (20)  / \       cos (10)  /
(cos⁡2(10−π2)cos⁡2(10)+1)cos⁡(20−π2)(1+cos⁡2(20−π2)cos⁡2(20))(−cos⁡2(10−π2)cos⁡2(10)+1)cos⁡(20)\frac{\left(\frac{\cos^{2}{\left(10 - \frac{\pi}{2} \right)}}{\cos^{2}{\left(10 \right)}} + 1\right) \cos{\left(20 - \frac{\pi}{2} \right)}}{\left(1 + \frac{\cos^{2}{\left(20 - \frac{\pi}{2} \right)}}{\cos^{2}{\left(20 \right)}}\right) \left(- \frac{\cos^{2}{\left(10 - \frac{\pi}{2} \right)}}{\cos^{2}{\left(10 \right)}} + 1\right) \cos{\left(20 \right)}} 
    /       2    \           
    \1 + tan (10)/*tan(20)   
-----------------------------
/       2    \ /       2    \
\1 + tan (20)/*\1 - tan (10)/
(tan⁡2(10)+1)tan⁡(20)(1−tan⁡2(10))(1+tan⁡2(20))\frac{\left(\tan^{2}{\left(10 \right)} + 1\right) \tan{\left(20 \right)}}{\left(1 - \tan^{2}{\left(10 \right)}\right) \left(1 + \tan^{2}{\left(20 \right)}\right)} 
    /       2    \            
    \1 + cot (10)/*cot(20)    
------------------------------
/       2    \ /        2    \
\1 + cot (20)/*\-1 + cot (10)/
(1+cot⁡2(10))cot⁡(20)(−1+cot⁡2(10))(cot⁡2(20)+1)\frac{\left(1 + \cot^{2}{\left(10 \right)}\right) \cot{\left(20 \right)}}{\left(-1 + \cot^{2}{\left(10 \right)}\right) \left(\cot^{2}{\left(20 \right)} + 1\right)} 
(1 + cot(10)^2)*cot(20)/((1 + cot(20)^2)*(-1 + cot(10)^2))
    © Sr Examen – Калькулятор