Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(8*a)*cot(8*a)-cos(x)^(26*a-1)/(1-sin(x)^26*a)
¿Cómo vas a descomponer esta tan(8*a)*cot(8*a)-cos(x)^(26*a-1)/(1-sin(x)^26*a) expresión en fracciones?
Solución
Ha introducido
[src]
26*a - 1
cos (x)
tan(8*a)*cot(8*a) - --------------
26
1 - sin (x)*a
$$\tan{\left(8 a \right)} \cot{\left(8 a \right)} - \frac{\cos^{26 a - 1}{\left(x \right)}}{- a \sin^{26}{\left(x \right)} + 1}$$
tan(8*a)*cot(8*a) - cos(x)^(26*a - 1)/(1 - sin(x)^26*a)
Simplificación general
[src]
-1 + 26*a 26
-1 + cos (x) + a*sin (x)
---------------------------------
26
-1 + a*sin (x)
$$\frac{a \sin^{26}{\left(x \right)} + \cos^{26 a - 1}{\left(x \right)} - 1}{a \sin^{26}{\left(x \right)} - 1}$$
(-1 + cos(x)^(-1 + 26*a) + a*sin(x)^26)/(-1 + a*sin(x)^26)
Respuesta numérica
[src]
cot(8*a)*tan(8*a) - cos(x)^(-1.0 + 26.0*a)/(1.0 - a*sin(x)^26)
cot(8*a)*tan(8*a) - cos(x)^(-1.0 + 26.0*a)/(1.0 - a*sin(x)^26)
Denominador común
[src]
26*a 26
cos (x) - cos(x)*cot(8*a)*tan(8*a) + a*sin (x)*cos(x)*cot(8*a)*tan(8*a)
---------------------------------------------------------------------------
26
-cos(x) + a*sin (x)*cos(x)
$$\frac{a \sin^{26}{\left(x \right)} \cos{\left(x \right)} \tan{\left(8 a \right)} \cot{\left(8 a \right)} - \cos{\left(x \right)} \tan{\left(8 a \right)} \cot{\left(8 a \right)} + \cos^{26 a}{\left(x \right)}}{a \sin^{26}{\left(x \right)} \cos{\left(x \right)} - \cos{\left(x \right)}}$$
(cos(x)^(26*a) - cos(x)*cot(8*a)*tan(8*a) + a*sin(x)^26*cos(x)*cot(8*a)*tan(8*a))/(-cos(x) + a*sin(x)^26*cos(x))
Denominador racional
[src]
-1 + 26*a 26
cos (x) - cot(8*a)*tan(8*a) + a*sin (x)*cot(8*a)*tan(8*a)
------------------------------------------------------------------
26
-1 + a*sin (x)
$$\frac{a \sin^{26}{\left(x \right)} \tan{\left(8 a \right)} \cot{\left(8 a \right)} + \cos^{26 a - 1}{\left(x \right)} - \tan{\left(8 a \right)} \cot{\left(8 a \right)}}{a \sin^{26}{\left(x \right)} - 1}$$
(cos(x)^(-1 + 26*a) - cot(8*a)*tan(8*a) + a*sin(x)^26*cot(8*a)*tan(8*a))/(-1 + a*sin(x)^26)
Combinatoria
[src]
26*a
cos (x) 26
---------- - cot(8*a)*tan(8*a) + a*sin (x)*cot(8*a)*tan(8*a)
cos(x)
-------------------------------------------------------------
26
-1 + a*sin (x)
$$\frac{a \sin^{26}{\left(x \right)} \tan{\left(8 a \right)} \cot{\left(8 a \right)} - \tan{\left(8 a \right)} \cot{\left(8 a \right)} + \frac{\cos^{26 a}{\left(x \right)}}{\cos{\left(x \right)}}}{a \sin^{26}{\left(x \right)} - 1}$$
(cos(x)^(26*a)/cos(x) - cot(8*a)*tan(8*a) + a*sin(x)^26*cot(8*a)*tan(8*a))/(-1 + a*sin(x)^26)
Unión de expresiones racionales
[src]
-1 + 26*a / 26 \
- cos (x) + \1 - a*sin (x)/*cot(8*a)*tan(8*a)
------------------------------------------------------
26
1 - a*sin (x)
$$\frac{\left(- a \sin^{26}{\left(x \right)} + 1\right) \tan{\left(8 a \right)} \cot{\left(8 a \right)} - \cos^{26 a - 1}{\left(x \right)}}{- a \sin^{26}{\left(x \right)} + 1}$$
(-cos(x)^(-1 + 26*a) + (1 - a*sin(x)^26)*cot(8*a)*tan(8*a))/(1 - a*sin(x)^26)
Potencias
[src]
-1 + 26*a
/ I*x -I*x\
|e e |
|---- + -----| / 8*I*a -8*I*a\
\ 2 2 / I*\- e + e /*cot(8*a)
- ------------------------ + -------------------------------
26 -8*I*a 8*I*a
/ -I*x I*x\ e + e
a*\- e + e /
1 + --------------------
67108864
$$\frac{i \left(- e^{8 i a} + e^{- 8 i a}\right) \cot{\left(8 a \right)}}{e^{8 i a} + e^{- 8 i a}} - \frac{\left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{26 a - 1}}{\frac{a \left(e^{i x} - e^{- i x}\right)^{26}}{67108864} + 1}$$
-(exp(i*x)/2 + exp(-i*x)/2)^(-1 + 26*a)/(1 + a*(-exp(-i*x) + exp(i*x))^26/67108864) + i*(-exp(8*i*a) + exp(-8*i*a))*cot(8*a)/(exp(-8*i*a) + exp(8*i*a))
Parte trigonométrica
[src]
-1 + 26*a/ pi\
sin |x + --|
\ 2 /
1 - --------------------
26
1 - a*sin (x)
$$1 - \frac{\sin^{26 a - 1}{\left(x + \frac{\pi}{2} \right)}}{- a \sin^{26}{\left(x \right)} + 1}$$
-1 + 26*a
/ 1 \
|------|
\sec(x)/
1 - -----------------
a
1 - -------------
26/ pi\
sec |x - --|
\ 2 /
$$1 - \frac{\left(\frac{1}{\sec{\left(x \right)}}\right)^{26 a - 1}}{- \frac{a}{\sec^{26}{\left(x - \frac{\pi}{2} \right)}} + 1}$$
-1 + 26*a
cos (x)
1 - ---------------
26
1 - a*sin (x)
$$1 - \frac{\cos^{26 a - 1}{\left(x \right)}}{- a \sin^{26}{\left(x \right)} + 1}$$
26*a - 1
cos (x)
1 - --------------
26
1 - a*sin (x)
$$1 - \frac{\cos^{26 a - 1}{\left(x \right)}}{- a \sin^{26}{\left(x \right)} + 1}$$
-1 + 26*a/ pi\
sin |x + --|
\ 2 /
1 - ---------------------------------------------
13 13
/ / pi\\ / / pi\\
1 - a*|1 - sin|x + --|| *|1 + sin|x + --||
\ \ 2 // \ \ 2 //
$$1 - \frac{\sin^{26 a - 1}{\left(x + \frac{\pi}{2} \right)}}{- a \left(1 - \sin{\left(x + \frac{\pi}{2} \right)}\right)^{13} \left(\sin{\left(x + \frac{\pi}{2} \right)} + 1\right)^{13} + 1}$$
-1 + 26*a
/ 1 \
|-----------|
| /pi \|
|csc|-- - x||
\ \2 //
1 - ----------------------
a
1 - --------
26
csc (x)
$$1 - \frac{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{26 a - 1}}{- \frac{a}{\csc^{26}{\left(x \right)}} + 1}$$
-1 + 26*a
/ 1 \
|------|
\sec(x)/
1 - -----------------------------------
13 13
/ 1 \ / 1 \
1 - a*|1 + ------| *|1 - ------|
\ sec(x)/ \ sec(x)/
$$1 - \frac{\left(\frac{1}{\sec{\left(x \right)}}\right)^{26 a - 1}}{- a \left(1 - \frac{1}{\sec{\left(x \right)}}\right)^{13} \left(1 + \frac{1}{\sec{\left(x \right)}}\right)^{13} + 1}$$
-1 + 26*a
cos (x)
1 - -----------------------------------
13 13
1 - a*(1 - cos(x)) *(1 + cos(x))
$$1 - \frac{\cos^{26 a - 1}{\left(x \right)}}{- a \left(1 - \cos{\left(x \right)}\right)^{13} \left(\cos{\left(x \right)} + 1\right)^{13} + 1}$$
-1 + 26*a
cos (x)
1 - -------------------
26/ pi\
1 - a*cos |x - --|
\ 2 /
$$1 - \frac{\cos^{26 a - 1}{\left(x \right)}}{- a \cos^{26}{\left(x - \frac{\pi}{2} \right)} + 1}$$
-1 + 26*a
/ 2/x\\
|1 - tan |-||
| \2/|
|-----------|
| 2/x\|
|1 + tan |-||
\ \2//
1 - ---------------------------------------------
13 13
/ 2/x\\ / 2/x\\
| 1 - tan |-|| | 1 - tan |-||
| \2/| | \2/|
1 - a*|1 + -----------| *|1 - -----------|
| 2/x\| | 2/x\|
| 1 + tan |-|| | 1 + tan |-||
\ \2// \ \2//
$$- \frac{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{26 a - 1}}{- a \left(- \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{13} \left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{13} + 1} + 1$$
-1 + 26*a
/ 2/x\\
|-1 + cot |-||
| \2/|
|------------|
| 2/x\ |
|1 + cot |-| |
\ \2/ /
1 - -----------------------
26/x\
67108864*a*cot |-|
\2/
1 - -------------------
26
/ 2/x\\
|1 + cot |-||
\ \2//
$$- \frac{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{26 a - 1}}{- \frac{67108864 a \cot^{26}{\left(\frac{x}{2} \right)}}{\left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{26}} + 1} + 1$$
-1 + 26*a
/ 1 \
|------|
\sec(x)/
1 - -----------------
a
1 - --------
26
csc (x)
$$1 - \frac{\left(\frac{1}{\sec{\left(x \right)}}\right)^{26 a - 1}}{- \frac{a}{\csc^{26}{\left(x \right)}} + 1}$$
-1 + 26*a
/ 2/x\\
|-1 + cot |-||
| \2/|
|------------|
| 2/x\ |
|1 + cot |-| |
\ \2/ /
1 - -----------------------------------------------
13 13
/ 2/x\\ / 2/x\\
| -1 + cot |-|| | -1 + cot |-||
| \2/| | \2/|
1 - a*|1 + ------------| *|1 - ------------|
| 2/x\ | | 2/x\ |
| 1 + cot |-| | | 1 + cot |-| |
\ \2/ / \ \2/ /
$$- \frac{\left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{26 a - 1}}{- a \left(- \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{13} \left(\frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1} + 1\right)^{13} + 1} + 1$$
-1 + 26*a
/ 2/x\\
|1 - tan |-||
| \2/|
|-----------|
| 2/x\|
|1 + tan |-||
\ \2//
1 - -----------------------
26/x\
67108864*a*tan |-|
\2/
1 - -------------------
26
/ 2/x\\
|1 + tan |-||
\ \2//
$$- \frac{\left(\frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}\right)^{26 a - 1}}{- \frac{67108864 a \tan^{26}{\left(\frac{x}{2} \right)}}{\left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{26}} + 1} + 1$$
-1 + 26*a
/ 1 \
|-----------|
| /pi \|
|csc|-- - x||
\ \2 //
1 - ---------------------------------------------
13 13
/ 1 \ / 1 \
1 - a*|1 + -----------| *|1 - -----------|
| /pi \| | /pi \|
| csc|-- - x|| | csc|-- - x||
\ \2 // \ \2 //
$$1 - \frac{\left(\frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{26 a - 1}}{- a \left(1 - \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{13} \left(1 + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}\right)^{13} + 1}$$
1 - (1/csc(pi/2 - x))^(-1 + 26*a)/(1 - a*(1 + 1/csc(pi/2 - x))^13*(1 - 1/csc(pi/2 - x))^13)