Descomposición de una fracción tan(p/(4+a))+tan(a-p/4)/tan(2*a) (tangente de (p dividir por (4 más a)) más tangente de (a menos p dividir por 4) dividir por tangente de (2 multiplicar por a))

Ha introducido [src]

                /    p\
             tan|a - -|
   /  p  \      \    4/
tan|-----| + ----------
   \4 + a/    tan(2*a)

\tan{\left(\frac{p}{a + 4} \right)} + \frac{\tan{\left(a - \frac{p}{4} \right)}}{\tan{\left(2 a \right)}}

tan(p/(4 + a)) + tan(a - p/4)/tan(2*a)

Respuesta numérica [src]

tan(a - p/4)/tan(2*a) + tan(p/(4 + a))

tan(a - p/4)/tan(2*a) + tan(p/(4 + a))

Unión de expresiones racionales [src]

            /  p  \      /-p + 4*a\
tan(2*a)*tan|-----| + tan|--------|
            \4 + a/      \   4    /
-----------------------------------
              tan(2*a)

\frac{\tan{\left(2 a \right)} \tan{\left(\frac{p}{a + 4} \right)} + \tan{\left(\frac{4 a - p}{4} \right)}}{\tan{\left(2 a \right)}}

(tan(2*a)*tan(p/(4 + a)) + tan((-p + 4*a)/4))/tan(2*a)

Potencias [src]

  /    I*p     -I*p \   /     /    p\      /     p\\                   
  |   -----    -----|   |   I*|a - -|    I*|-a + -||                   
  |   4 + a    4 + a|   |     \    4/      \     4/| / -2*I*a    2*I*a\
I*\- e      + e     /   \- e          + e          /*\e       + e     /
--------------------- + -----------------------------------------------
     I*p     -I*p                            /   /    p\      /     p\\
    -----    -----                           | I*|a - -|    I*|-a + -||
    4 + a    4 + a      /   2*I*a    -2*I*a\ |   \    4/      \     4/|
   e      + e           \- e      + e      /*\e          + e          /

\frac{i \left(- e^{\frac{i p}{a + 4}} + e^{- \frac{i p}{a + 4}}\right)}{e^{\frac{i p}{a + 4}} + e^{- \frac{i p}{a + 4}}} + \frac{\left(e^{2 i a} + e^{- 2 i a}\right) \left(e^{i \left(- a + \frac{p}{4}\right)} - e^{i \left(a - \frac{p}{4}\right)}\right)}{\left(- e^{2 i a} + e^{- 2 i a}\right) \left(e^{i \left(- a + \frac{p}{4}\right)} + e^{i \left(a - \frac{p}{4}\right)}\right)}

i*(-exp(i*p/(4 + a)) + exp(-i*p/(4 + a)))/(exp(i*p/(4 + a)) + exp(-i*p/(4 + a))) + (-exp(i*(a - p/4)) + exp(i*(-a + p/4)))*(exp(-2*i*a) + exp(2*i*a))/((-exp(2*i*a) + exp(-2*i*a))*(exp(i*(a - p/4)) + exp(i*(-a + p/4))))

Denominador racional [src]

            /  p  \      /    p\
tan(2*a)*tan|-----| + tan|a - -|
            \4 + a/      \    4/
--------------------------------
            tan(2*a)

\frac{\tan{\left(2 a \right)} \tan{\left(\frac{p}{a + 4} \right)} + \tan{\left(a - \frac{p}{4} \right)}}{\tan{\left(2 a \right)}}

(tan(2*a)*tan(p/(4 + a)) + tan(a - p/4))/tan(2*a)

Abrimos la expresión [src]

                                                                          /p\                       2       /p\                   
                                           3                           tan|-|                    tan (a)*tan|-|                   
           tan(a)                       tan (a)                           \4/                               \4/            /  p  \
--------------------------- - --------------------------- - --------------------------- + --------------------------- + tan|-----|
                2       /p\                   2       /p\                   2       /p\                   2       /p\      \4 + a/
2*tan(a) + 2*tan (a)*tan|-|   2*tan(a) + 2*tan (a)*tan|-|   2*tan(a) + 2*tan (a)*tan|-|   2*tan(a) + 2*tan (a)*tan|-|             
                        \4/                           \4/                           \4/                           \4/

\tan{\left(\frac{p}{a + 4} \right)} - \frac{\tan^{3}{\left(a \right)}}{2 \tan^{2}{\left(a \right)} \tan{\left(\frac{p}{4} \right)} + 2 \tan{\left(a \right)}} + \frac{\tan^{2}{\left(a \right)} \tan{\left(\frac{p}{4} \right)}}{2 \tan^{2}{\left(a \right)} \tan{\left(\frac{p}{4} \right)} + 2 \tan{\left(a \right)}} + \frac{\tan{\left(a \right)}}{2 \tan^{2}{\left(a \right)} \tan{\left(\frac{p}{4} \right)} + 2 \tan{\left(a \right)}} - \frac{\tan{\left(\frac{p}{4} \right)}}{2 \tan^{2}{\left(a \right)} \tan{\left(\frac{p}{4} \right)} + 2 \tan{\left(a \right)}}

tan(a)/(2*tan(a) + 2*tan(a)^2*tan(p/4)) - tan(a)^3/(2*tan(a) + 2*tan(a)^2*tan(p/4)) - tan(p/4)/(2*tan(a) + 2*tan(a)^2*tan(p/4)) + tan(a)^2*tan(p/4)/(2*tan(a) + 2*tan(a)^2*tan(p/4)) + tan(p/(4 + a))

Combinatoria [src]

            /  p  \      /    p\
tan(2*a)*tan|-----| + tan|a - -|
            \4 + a/      \    4/
--------------------------------
            tan(2*a)

\frac{\tan{\left(2 a \right)} \tan{\left(\frac{p}{a + 4} \right)} + \tan{\left(a - \frac{p}{4} \right)}}{\tan{\left(2 a \right)}}

(tan(2*a)*tan(p/(4 + a)) + tan(a - p/4))/tan(2*a)

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¿Cómo vas a descomponer esta tan(p/(4+a))+tan(a-p/4)/tan(2*a) expresión en fracciones?

Solución