Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan2αc2α-(1-sin^25α)/(cos^25α-1)
¿Cómo vas a descomponer esta tan2αc2α-(1-sin^25α)/(cos^25α-1) expresión en fracciones?
Solución
Ha introducido
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25
1 - sin (a)
tan(2*a)*c2*a - ------------
25
cos (a) - 1
$$a c_{2} \tan{\left(2 a \right)} - \frac{1 - \sin^{25}{\left(a \right)}}{\cos^{25}{\left(a \right)} - 1}$$
(tan(2*a)*c2)*a - (1 - sin(a)^25)/(cos(a)^25 - 1)
Simplificación general
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25 / 25 \
-1 + sin (a) + a*c2*\-1 + cos (a)/*tan(2*a)
---------------------------------------------
25
-1 + cos (a)
$$\frac{a c_{2} \left(\cos^{25}{\left(a \right)} - 1\right) \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$
(-1 + sin(a)^25 + a*c2*(-1 + cos(a)^25)*tan(2*a))/(-1 + cos(a)^25)
Denominador común
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25
-1 + sin (a)
------------- + a*c2*tan(2*a)
25
-1 + cos (a)
$$a c_{2} \tan{\left(2 a \right)} + \frac{\sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$
(-1 + sin(a)^25)/(-1 + cos(a)^25) + a*c2*tan(2*a)
Unión de expresiones racionales
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25 / 25 \
-1 + sin (a) + a*c2*\-1 + cos (a)/*tan(2*a)
---------------------------------------------
25
-1 + cos (a)
$$\frac{a c_{2} \left(\cos^{25}{\left(a \right)} - 1\right) \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$
(-1 + sin(a)^25 + a*c2*(-1 + cos(a)^25)*tan(2*a))/(-1 + cos(a)^25)
Denominador racional
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25 / 25 \
-1 + sin (a) + a*c2*\-1 + cos (a)/*tan(2*a)
---------------------------------------------
25
-1 + cos (a)
$$\frac{a c_{2} \left(\cos^{25}{\left(a \right)} - 1\right) \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$
(-1 + sin(a)^25 + a*c2*(-1 + cos(a)^25)*tan(2*a))/(-1 + cos(a)^25)
Respuesta numérica
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-(1.0 - sin(a)^25)/(-1.0 + cos(a)^25) + a*c2*tan(2*a)
-(1.0 - sin(a)^25)/(-1.0 + cos(a)^25) + a*c2*tan(2*a)
Potencias
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25
/ -I*a I*a\
I*\- e + e /
1 + -------------------- / 2*I*a -2*I*a\
33554432 I*a*c2*\- e + e /
- ------------------------ + ---------------------------
25 -2*I*a 2*I*a
/ I*a -I*a\ e + e
|e e |
-1 + |---- + -----|
\ 2 2 /
$$\frac{i a c_{2} \left(- e^{2 i a} + e^{- 2 i a}\right)}{e^{2 i a} + e^{- 2 i a}} - \frac{\frac{i \left(e^{i a} - e^{- i a}\right)^{25}}{33554432} + 1}{\left(\frac{e^{i a}}{2} + \frac{e^{- i a}}{2}\right)^{25} - 1}$$
25
-1 + sin (a)
------------- + a*c2*tan(2*a)
25
-1 + cos (a)
$$a c_{2} \tan{\left(2 a \right)} + \frac{\sin^{25}{\left(a \right)} - 1}{\cos^{25}{\left(a \right)} - 1}$$
(-1 + sin(a)^25)/(-1 + cos(a)^25) + a*c2*tan(2*a)
Combinatoria
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25 25
-1 + sin (a) - a*c2*tan(2*a) + a*c2*cos (a)*tan(2*a)
-------------------------------------------------------------------------------------------------------
/ 2 3 4 \ / 5 10 15 20 \
(-1 + cos(a))*\1 + cos (a) + cos (a) + cos (a) + cos(a)/*\1 + cos (a) + cos (a) + cos (a) + cos (a)/
$$\frac{a c_{2} \cos^{25}{\left(a \right)} \tan{\left(2 a \right)} - a c_{2} \tan{\left(2 a \right)} + \sin^{25}{\left(a \right)} - 1}{\left(\cos{\left(a \right)} - 1\right) \left(\cos^{4}{\left(a \right)} + \cos^{3}{\left(a \right)} + \cos^{2}{\left(a \right)} + \cos{\left(a \right)} + 1\right) \left(\cos^{20}{\left(a \right)} + \cos^{15}{\left(a \right)} + \cos^{10}{\left(a \right)} + \cos^{5}{\left(a \right)} + 1\right)}$$
(-1 + sin(a)^25 - a*c2*tan(2*a) + a*c2*cos(a)^25*tan(2*a))/((-1 + cos(a))*(1 + cos(a)^2 + cos(a)^3 + cos(a)^4 + cos(a))*(1 + cos(a)^5 + cos(a)^10 + cos(a)^15 + cos(a)^20))