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Simplificación de expresiones/ Descomposición en fracciones simples/ tg(4a)ctg(4a)-(1-cos^2(9a))/(sin^2(9a)-1)

¿Cómo vas a descomponer esta tg(4a)ctg(4a)-(1-cos^2(9a))/(sin^2(9a)-1) expresión en fracciones?

Expresión a simplificar:

Solución

Ha introducido [src] 
                           2     
                    1 - cos (9*a)
tan(4*a)*cot(4*a) - -------------
                       2         
                    sin (9*a) - 1
−1−cos⁡2(9a)sin⁡2(9a)−1+tan⁡(4a)cot⁡(4a)- \frac{1 - \cos^{2}{\left(9 a \right)}}{\sin^{2}{\left(9 a \right)} - 1} + \tan{\left(4 a \right)} \cot{\left(4 a \right)} 
tan(4*a)*cot(4*a) - (1 - cos(9*a)^2)/(sin(9*a)^2 - 1)
Simplificación general [src] 
    1    
---------
   2     
cos (9*a)
1cos⁡2(9a)\frac{1}{\cos^{2}{\left(9 a \right)}} 
cos(9*a)^(-2)
Denominador común [src] 
        2                         
-1 + cos (9*a)                    
-------------- + cot(4*a)*tan(4*a)
        2                         
-1 + sin (9*a)
tan⁡(4a)cot⁡(4a)+cos⁡2(9a)−1sin⁡2(9a)−1\tan{\left(4 a \right)} \cot{\left(4 a \right)} + \frac{\cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1} 
(-1 + cos(9*a)^2)/(-1 + sin(9*a)^2) + cot(4*a)*tan(4*a)
Abrimos la expresión [src] 
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                                                                             1                                                                                                                                                   559104*cos  (a)                                                                                                                                            294912*cos  (a)                                                                                                                                             114048*cos (a)                                                                                                                                              2160*cos (a)                                                                                                                       4*tan (a)                                                                                                4*tan(a)                                                                                                                        81*cos (a)                                                                                                                                               22176*cos (a)                                                                                                                                              65536*cos  (a)                                                                                                                                            329472*cos  (a)                                                                                                                                            552960*cos  (a)                                                                                                                  24*cot (a)*tan(a)                                                                                       4*cot (a)*tan (a)                                                                                        4*cot (a)*tan(a)                                                                                       24*cot (a)*tan (a)                                         
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                 12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                       3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2                            12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                     12                16                8              4            2               6               18                10                14                       3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2                              3            3       2           4                  3       4            2          
  -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -1 - 559104*sin  (a) - 294912*sin  (a) - 114048*sin (a) - 2160*sin (a) + 81*sin (a) + 22176*sin (a) + 65536*sin  (a) + 329472*sin  (a) + 552960*sin  (a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)   -4*cot(a) + 4*cot (a) - 24*cot (a)*tan (a) - 4*tan (a)*cot(a) + 4*cot (a)*tan (a) + 24*tan (a)*cot(a)
65536cos⁡18(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1−294912cos⁡16(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1+552960cos⁡14(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1−559104cos⁡12(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1+329472cos⁡10(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1−114048cos⁡8(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1+22176cos⁡6(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1−2160cos⁡4(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1+81cos⁡2(a)65536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1−165536sin⁡18(a)−294912sin⁡16(a)+552960sin⁡14(a)−559104sin⁡12(a)+329472sin⁡10(a)−114048sin⁡8(a)+22176sin⁡6(a)−2160sin⁡4(a)+81sin⁡2(a)−1−4tan⁡3(a)cot⁡4(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)+24tan⁡3(a)cot⁡2(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)−4tan⁡3(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)+4tan⁡(a)cot⁡4(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)−24tan⁡(a)cot⁡2(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)+4tan⁡(a)4tan⁡4(a)cot⁡3(a)−4tan⁡4(a)cot⁡(a)−24tan⁡2(a)cot⁡3(a)+24tan⁡2(a)cot⁡(a)+4cot⁡3(a)−4cot⁡(a)\frac{65536 \cos^{18}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} - \frac{294912 \cos^{16}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} + \frac{552960 \cos^{14}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} - \frac{559104 \cos^{12}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} + \frac{329472 \cos^{10}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} - \frac{114048 \cos^{8}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} + \frac{22176 \cos^{6}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} - \frac{2160 \cos^{4}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} + \frac{81 \cos^{2}{\left(a \right)}}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} - \frac{1}{65536 \sin^{18}{\left(a \right)} - 294912 \sin^{16}{\left(a \right)} + 552960 \sin^{14}{\left(a \right)} - 559104 \sin^{12}{\left(a \right)} + 329472 \sin^{10}{\left(a \right)} - 114048 \sin^{8}{\left(a \right)} + 22176 \sin^{6}{\left(a \right)} - 2160 \sin^{4}{\left(a \right)} + 81 \sin^{2}{\left(a \right)} - 1} - \frac{4 \tan^{3}{\left(a \right)} \cot^{4}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} + \frac{24 \tan^{3}{\left(a \right)} \cot^{2}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} - \frac{4 \tan^{3}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} + \frac{4 \tan{\left(a \right)} \cot^{4}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} - \frac{24 \tan{\left(a \right)} \cot^{2}{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} + \frac{4 \tan{\left(a \right)}}{4 \tan^{4}{\left(a \right)} \cot^{3}{\left(a \right)} - 4 \tan^{4}{\left(a \right)} \cot{\left(a \right)} - 24 \tan^{2}{\left(a \right)} \cot^{3}{\left(a \right)} + 24 \tan^{2}{\left(a \right)} \cot{\left(a \right)} + 4 \cot^{3}{\left(a \right)} - 4 \cot{\left(a \right)}} 
-1/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) - 559104*cos(a)^12/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) - 294912*cos(a)^16/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) - 114048*cos(a)^8/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) - 2160*cos(a)^4/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) - 4*tan(a)^3/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 4*tan(a)/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 81*cos(a)^2/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) + 22176*cos(a)^6/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) + 65536*cos(a)^18/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) + 329472*cos(a)^10/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) + 552960*cos(a)^14/(-1 - 559104*sin(a)^12 - 294912*sin(a)^16 - 114048*sin(a)^8 - 2160*sin(a)^4 + 81*sin(a)^2 + 22176*sin(a)^6 + 65536*sin(a)^18 + 329472*sin(a)^10 + 552960*sin(a)^14) - 24*cot(a)^2*tan(a)/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) - 4*cot(a)^4*tan(a)^3/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 4*cot(a)^4*tan(a)/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a)) + 24*cot(a)^2*tan(a)^3/(-4*cot(a) + 4*cot(a)^3 - 24*cot(a)^3*tan(a)^2 - 4*tan(a)^4*cot(a) + 4*cot(a)^3*tan(a)^4 + 24*tan(a)^2*cot(a))
Denominador racional [src] 
        2        /        2     \                  
-1 + cos (9*a) + \-1 + sin (9*a)/*cot(4*a)*tan(4*a)
---------------------------------------------------
                           2                       
                   -1 + sin (9*a)
(sin⁡2(9a)−1)tan⁡(4a)cot⁡(4a)+cos⁡2(9a)−1sin⁡2(9a)−1\frac{\left(\sin^{2}{\left(9 a \right)} - 1\right) \tan{\left(4 a \right)} \cot{\left(4 a \right)} + \cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1} 
(-1 + cos(9*a)^2 + (-1 + sin(9*a)^2)*cot(4*a)*tan(4*a))/(-1 + sin(9*a)^2)
Parte trigonométrica [src] 
           2/pi      \
    1 - sin |-- + 9*a|
            \2       /
1 - ------------------
              2       
      -1 + sin (9*a)
−1−sin⁡2(9a+π2)sin⁡2(9a)−1+1- \frac{1 - \sin^{2}{\left(9 a + \frac{\pi}{2} \right)}}{\sin^{2}{\left(9 a \right)} - 1} + 1 
                        2
         /       2/9*a\\ 
         |1 - tan |---|| 
         \        \ 2 // 
     1 - ----------------
                        2
         /       2/9*a\\ 
         |1 + tan |---|| 
         \        \ 2 // 
1 - ---------------------
                2/9*a\   
           4*tan |---|   
                 \ 2 /   
    -1 + ----------------
                        2
         /       2/9*a\\ 
         |1 + tan |---|| 
         \        \ 2 //
1−−(1−tan⁡2(9a2))2(tan⁡2(9a2)+1)2+1−1+4tan⁡2(9a2)(tan⁡2(9a2)+1)21 - \frac{- \frac{\left(1 - \tan^{2}{\left(\frac{9 a}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}} + 1}{-1 + \frac{4 \tan^{2}{\left(\frac{9 a}{2} \right)}}{\left(\tan^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}} 
      2      
-------------
1 + cos(18*a)
2cos⁡(18a)+1\frac{2}{\cos{\left(18 a \right)} + 1} 
           2      
    1 - cos (9*a) 
1 - --------------
            2     
    -1 + sin (9*a)
−1−cos⁡2(9a)sin⁡2(9a)−1+1- \frac{1 - \cos^{2}{\left(9 a \right)}}{\sin^{2}{\left(9 a \right)} - 1} + 1 
               2
/       2/9*a\\ 
|1 + tan |---|| 
\        \ 2 // 
----------------
               2
/       2/9*a\\ 
|1 - tan |---|| 
\        \ 2 //
(tan⁡2(9a2)+1)2(1−tan⁡2(9a2))2\frac{\left(\tan^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{9 a}{2} \right)}\right)^{2}} 
                        2
        /        2/9*a\\ 
        |-1 + cot |---|| 
        \         \ 2 // 
    1 - -----------------
                        2
         /       2/9*a\\ 
         |1 + cot |---|| 
         \        \ 2 // 
1 - ---------------------
                2/9*a\   
           4*cot |---|   
                 \ 2 /   
    -1 + ----------------
                        2
         /       2/9*a\\ 
         |1 + cot |---|| 
         \        \ 2 //
1−−(cot⁡2(9a2)−1)2(cot⁡2(9a2)+1)2+1−1+4cot⁡2(9a2)(cot⁡2(9a2)+1)21 - \frac{- \frac{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}} + 1}{-1 + \frac{4 \cot^{2}{\left(\frac{9 a}{2} \right)}}{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}} 
              2        
       1 - cos (9*a)   
1 - -------------------
            2/      pi\
    -1 + cos |9*a - --|
             \      2 /
−1−cos⁡2(9a)cos⁡2(9a−π2)−1+1- \frac{1 - \cos^{2}{\left(9 a \right)}}{\cos^{2}{\left(9 a - \frac{\pi}{2} \right)} - 1} + 1 
              1       
    1 - --------------
           2/pi      \
        csc |-- - 9*a|
            \2       /
1 - ------------------
               1      
      -1 + ---------  
              2       
           csc (9*a)
1−1−1csc⁡2(−9a+π2)−1+1csc⁡2(9a)1 - \frac{1 - \frac{1}{\csc^{2}{\left(- 9 a + \frac{\pi}{2} \right)}}}{-1 + \frac{1}{\csc^{2}{\left(9 a \right)}}} 
               1       
       1 - ---------   
              2        
           sec (9*a)   
1 - -------------------
               1       
    -1 + --------------
            2/      pi\
         sec |9*a - --|
             \      2 /
1−1−1sec⁡2(9a)−1+1sec⁡2(9a−π2)1 - \frac{1 - \frac{1}{\sec^{2}{\left(9 a \right)}}}{-1 + \frac{1}{\sec^{2}{\left(9 a - \frac{\pi}{2} \right)}}} 
            1     
    1 - --------- 
           2      
        sec (9*a) 
1 - --------------
             1    
    -1 + ---------
            2     
         csc (9*a)
1−1−1sec⁡2(9a)−1+1csc⁡2(9a)1 - \frac{1 - \frac{1}{\sec^{2}{\left(9 a \right)}}}{-1 + \frac{1}{\csc^{2}{\left(9 a \right)}}} 
                2
 /       2/9*a\\ 
 |1 + cot |---|| 
 \        \ 2 // 
-----------------
                2
/        2/9*a\\ 
|-1 + cot |---|| 
\         \ 2 //
(cot⁡2(9a2)+1)2(cot⁡2(9a2)−1)2\frac{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} - 1\right)^{2}} 
   2/pi      \
csc |-- - 9*a|
    \2       /
csc⁡2(−9a+π2)\csc^{2}{\left(- 9 a + \frac{\pi}{2} \right)} 
      1       
--------------
   2/pi      \
sin |-- + 9*a|
    \2       /
1sin⁡2(9a+π2)\frac{1}{\sin^{2}{\left(9 a + \frac{\pi}{2} \right)}} 
   2     
sec (9*a)
sec⁡2(9a)\sec^{2}{\left(9 a \right)} 
    1    
---------
   2     
cos (9*a)
1cos⁡2(9a)\frac{1}{\cos^{2}{\left(9 a \right)}} 
cos(9*a)^(-2)
Respuesta numérica [src] 
cot(4*a)*tan(4*a) - (1.0 - cos(9*a)^2)/(-1.0 + sin(9*a)^2)
cot(4*a)*tan(4*a) - (1.0 - cos(9*a)^2)/(-1.0 + sin(9*a)^2)
Potencias [src] 
        2                         
-1 + cos (9*a)                    
-------------- + cot(4*a)*tan(4*a)
        2                         
-1 + sin (9*a)
tan⁡(4a)cot⁡(4a)+cos⁡2(9a)−1sin⁡2(9a)−1\tan{\left(4 a \right)} \cot{\left(4 a \right)} + \frac{\cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1} 
                         2                                    
       / -9*I*a    9*I*a\                                     
       |e         e     |                                     
   1 - |------- + ------|        /   4*I*a    -4*I*a\         
       \   2        2   /      I*\- e      + e      /*cot(4*a)
- -------------------------- + -------------------------------
                           2            -4*I*a    4*I*a       
       /   -9*I*a    9*I*a\            e       + e            
       \- e       + e     /                                   
  -1 - ---------------------                                  
                 4
−1−(e9ia2+e−9ia2)2−(e9ia−e−9ia)24−1+i(−e4ia+e−4ia)cot⁡(4a)e4ia+e−4ia- \frac{1 - \left(\frac{e^{9 i a}}{2} + \frac{e^{- 9 i a}}{2}\right)^{2}}{- \frac{\left(e^{9 i a} - e^{- 9 i a}\right)^{2}}{4} - 1} + \frac{i \left(- e^{4 i a} + e^{- 4 i a}\right) \cot{\left(4 a \right)}}{e^{4 i a} + e^{- 4 i a}} 
-(1 - (exp(-9*i*a)/2 + exp(9*i*a)/2)^2)/(-1 - (-exp(-9*i*a) + exp(9*i*a))^2/4) + i*(-exp(4*i*a) + exp(-4*i*a))*cot(4*a)/(exp(-4*i*a) + exp(4*i*a))
Unión de expresiones racionales [src] 
        2        /        2     \                  
-1 + cos (9*a) + \-1 + sin (9*a)/*cot(4*a)*tan(4*a)
---------------------------------------------------
                           2                       
                   -1 + sin (9*a)
(sin⁡2(9a)−1)tan⁡(4a)cot⁡(4a)+cos⁡2(9a)−1sin⁡2(9a)−1\frac{\left(\sin^{2}{\left(9 a \right)} - 1\right) \tan{\left(4 a \right)} \cot{\left(4 a \right)} + \cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1} 
(-1 + cos(9*a)^2 + (-1 + sin(9*a)^2)*cot(4*a)*tan(4*a))/(-1 + sin(9*a)^2)
Combinatoria [src] 
        2                               2                       
-1 + cos (9*a) - cot(4*a)*tan(4*a) + sin (9*a)*cot(4*a)*tan(4*a)
----------------------------------------------------------------
                 (1 + sin(9*a))*(-1 + sin(9*a))
sin⁡2(9a)tan⁡(4a)cot⁡(4a)+cos⁡2(9a)−tan⁡(4a)cot⁡(4a)−1(sin⁡(9a)−1)(sin⁡(9a)+1)\frac{\sin^{2}{\left(9 a \right)} \tan{\left(4 a \right)} \cot{\left(4 a \right)} + \cos^{2}{\left(9 a \right)} - \tan{\left(4 a \right)} \cot{\left(4 a \right)} - 1}{\left(\sin{\left(9 a \right)} - 1\right) \left(\sin{\left(9 a \right)} + 1\right)} 
(-1 + cos(9*a)^2 - cot(4*a)*tan(4*a) + sin(9*a)^2*cot(4*a)*tan(4*a))/((1 + sin(9*a))*(-1 + sin(9*a)))
    © Sr Examen – Калькулятор