Sr Examen
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?
Solución
Ha introducido
[src]
2
1 - cos (9*a)
tan(4*a)*cot(4*a) - -------------
2
sin (9*a) - 1
$$- \frac{1 - \cos^{2}{\left(9 a \right)}}{\sin^{2}{\left(9 a \right)} - 1} + \tan{\left(4 a \right)} \cot{\left(4 a \right)}$$
tan(4*a)*cot(4*a) - (1 - cos(9*a)^2)/(sin(9*a)^2 - 1)
Simplificación general
[src]
1 --------- 2 cos (9*a)
$$\frac{1}{\cos^{2}{\left(9 a \right)}}$$
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)
Denominador común
[src]
2
-1 + cos (9*a)
-------------- + cot(4*a)*tan(4*a)
2
-1 + sin (9*a)
$$\tan{\left(4 a \right)} \cot{\left(4 a \right)} + \frac{\cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1}$$
(-1 + cos(9*a)^2)/(-1 + sin(9*a)^2) + cot(4*a)*tan(4*a)
Potencias
[src]
2
-1 + cos (9*a)
-------------- + cot(4*a)*tan(4*a)
2
-1 + sin (9*a)
$$\tan{\left(4 a \right)} \cot{\left(4 a \right)} + \frac{\cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1}$$
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
$$- \frac{1 - \left(\frac{e^{9 i a}}{2} + \frac{e^{- 9 i a}}{2}\right)^{2}}{- \frac{\left(e^{9 i a} - e^{- 9 i a}\right)^{2}}{4} - 1} + \frac{i \left(- e^{4 i a} + e^{- 4 i a}\right) \cot{\left(4 a \right)}}{e^{4 i a} + e^{- 4 i a}}$$
-(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))
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))
$$\frac{\sin^{2}{\left(9 a \right)} \tan{\left(4 a \right)} \cot{\left(4 a \right)} + \cos^{2}{\left(9 a \right)} - \tan{\left(4 a \right)} \cot{\left(4 a \right)} - 1}{\left(\sin{\left(9 a \right)} - 1\right) \left(\sin{\left(9 a \right)} + 1\right)}$$
(-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)))
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)
$$\frac{\left(\sin^{2}{\left(9 a \right)} - 1\right) \tan{\left(4 a \right)} \cot{\left(4 a \right)} + \cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1}$$
(-1 + cos(9*a)^2 + (-1 + sin(9*a)^2)*cot(4*a)*tan(4*a))/(-1 + sin(9*a)^2)
Denominador racional
[src]
2 / 2 \
-1 + cos (9*a) + \-1 + sin (9*a)/*cot(4*a)*tan(4*a)
---------------------------------------------------
2
-1 + sin (9*a)
$$\frac{\left(\sin^{2}{\left(9 a \right)} - 1\right) \tan{\left(4 a \right)} \cot{\left(4 a \right)} + \cos^{2}{\left(9 a \right)} - 1}{\sin^{2}{\left(9 a \right)} - 1}$$
(-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)
$$- \frac{1 - \sin^{2}{\left(9 a + \frac{\pi}{2} \right)}}{\sin^{2}{\left(9 a \right)} - 1} + 1$$
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 //
$$1 - \frac{- \frac{\left(1 - \tan^{2}{\left(\frac{9 a}{2} \right)}\right)^{2}}{\left(\tan^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}} + 1}{-1 + \frac{4 \tan^{2}{\left(\frac{9 a}{2} \right)}}{\left(\tan^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}}$$
2 ------------- 1 + cos(18*a)
$$\frac{2}{\cos{\left(18 a \right)} + 1}$$
2
1 - cos (9*a)
1 - --------------
2
-1 + sin (9*a)
$$- \frac{1 - \cos^{2}{\left(9 a \right)}}{\sin^{2}{\left(9 a \right)} - 1} + 1$$
2
/ 2/9*a\\
|1 + tan |---||
\ \ 2 //
----------------
2
/ 2/9*a\\
|1 - tan |---||
\ \ 2 //
$$\frac{\left(\tan^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}{\left(1 - \tan^{2}{\left(\frac{9 a}{2} \right)}\right)^{2}}$$
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 //
$$1 - \frac{- \frac{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} - 1\right)^{2}}{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}} + 1}{-1 + \frac{4 \cot^{2}{\left(\frac{9 a}{2} \right)}}{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}}$$
2
1 - cos (9*a)
1 - -------------------
2/ pi\
-1 + cos |9*a - --|
\ 2 /
$$- \frac{1 - \cos^{2}{\left(9 a \right)}}{\cos^{2}{\left(9 a - \frac{\pi}{2} \right)} - 1} + 1$$
1
1 - --------------
2/pi \
csc |-- - 9*a|
\2 /
1 - ------------------
1
-1 + ---------
2
csc (9*a)
$$1 - \frac{1 - \frac{1}{\csc^{2}{\left(- 9 a + \frac{\pi}{2} \right)}}}{-1 + \frac{1}{\csc^{2}{\left(9 a \right)}}}$$
1
1 - ---------
2
sec (9*a)
1 - -------------------
1
-1 + --------------
2/ pi\
sec |9*a - --|
\ 2 /
$$1 - \frac{1 - \frac{1}{\sec^{2}{\left(9 a \right)}}}{-1 + \frac{1}{\sec^{2}{\left(9 a - \frac{\pi}{2} \right)}}}$$
1
1 - ---------
2
sec (9*a)
1 - --------------
1
-1 + ---------
2
csc (9*a)
$$1 - \frac{1 - \frac{1}{\sec^{2}{\left(9 a \right)}}}{-1 + \frac{1}{\csc^{2}{\left(9 a \right)}}}$$
2
/ 2/9*a\\
|1 + cot |---||
\ \ 2 //
-----------------
2
/ 2/9*a\\
|-1 + cot |---||
\ \ 2 //
$$\frac{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} + 1\right)^{2}}{\left(\cot^{2}{\left(\frac{9 a}{2} \right)} - 1\right)^{2}}$$
2/pi \
csc |-- - 9*a|
\2 /
$$\csc^{2}{\left(- 9 a + \frac{\pi}{2} \right)}$$
1
--------------
2/pi \
sin |-- + 9*a|
\2 /
$$\frac{1}{\sin^{2}{\left(9 a + \frac{\pi}{2} \right)}}$$
2 sec (9*a)
$$\sec^{2}{\left(9 a \right)}$$
1 --------- 2 cos (9*a)
$$\frac{1}{\cos^{2}{\left(9 a \right)}}$$
cos(9*a)^(-2)