Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
tan(a)/(1-tan(a)^(2))+cot(a)/(1-cot(2*a))
¿Cómo vas a descomponer esta tan(a)/(1-tan(a)^(2))+cot(a)/(1-cot(2*a)) expresión en fracciones?
Solución
Ha introducido
[src]
tan(a) cot(a)
----------- + ------------
2 1 - cot(2*a)
1 - tan (a)
$$\frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}} + \frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
tan(a)/(1 - tan(a)^2) + cot(a)/(1 - cot(2*a))
Simplificación general
[src]
1 tan(a)
------ - --------
tan(a) tan(2*a)
------------------------------
/ 2 \
\-1 + tan (a)/*(-1 + cot(2*a))
$$\frac{- \frac{\tan{\left(a \right)}}{\tan{\left(2 a \right)}} + \frac{1}{\tan{\left(a \right)}}}{\left(\tan^{2}{\left(a \right)} - 1\right) \left(\cot{\left(2 a \right)} - 1\right)}$$
(1/tan(a) - tan(a)/tan(2*a))/((-1 + tan(a)^2)*(-1 + cot(2*a)))
Respuesta numérica
[src]
tan(a)/(1.0 - tan(a)^2) + cot(a)/(1.0 - cot(2*a))
tan(a)/(1.0 - tan(a)^2) + cot(a)/(1.0 - cot(2*a))
Combinatoria
[src]
/ 2 \
-\-cot(a) - tan(a) + tan (a)*cot(a) + cot(2*a)*tan(a)/
-------------------------------------------------------
(1 + tan(a))*(-1 + cot(2*a))*(-1 + tan(a))
$$- \frac{\tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan{\left(a \right)} \cot{\left(2 a \right)} - \tan{\left(a \right)} - \cot{\left(a \right)}}{\left(\tan{\left(a \right)} - 1\right) \left(\tan{\left(a \right)} + 1\right) \left(\cot{\left(2 a \right)} - 1\right)}$$
-(-cot(a) - tan(a) + tan(a)^2*cot(a) + cot(2*a)*tan(a))/((1 + tan(a))*(-1 + cot(2*a))*(-1 + tan(a)))
Denominador racional
[src]
/ 2 \
\1 - tan (a)/*cot(a) + (1 - cot(2*a))*tan(a)
--------------------------------------------
/ 2 \
\1 - tan (a)/*(1 - cot(2*a))
$$\frac{\left(1 - \tan^{2}{\left(a \right)}\right) \cot{\left(a \right)} + \left(1 - \cot{\left(2 a \right)}\right) \tan{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \left(1 - \cot{\left(2 a \right)}\right)}$$
((1 - tan(a)^2)*cot(a) + (1 - cot(2*a))*tan(a))/((1 - tan(a)^2)*(1 - cot(2*a)))
Unión de expresiones racionales
[src]
/ 2 \
\1 - tan (a)/*cot(a) + (1 - cot(2*a))*tan(a)
--------------------------------------------
/ 2 \
\1 - tan (a)/*(1 - cot(2*a))
$$\frac{\left(1 - \tan^{2}{\left(a \right)}\right) \cot{\left(a \right)} + \left(1 - \cot{\left(2 a \right)}\right) \tan{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \left(1 - \cot{\left(2 a \right)}\right)}$$
((1 - tan(a)^2)*cot(a) + (1 - cot(2*a))*tan(a))/((1 - tan(a)^2)*(1 - cot(2*a)))
Parte trigonométrica
[src]
___ / 1 \ / pi\
\/ 2 *|1 + --------|*sec|2*a + --|
sec(2*a) \ sec(2*a)/ \ 4 /
--------------- - ----------------------------------
/ pi\ 2
2*sec|2*a - --|
\ 2 /
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\sec{\left(2 a \right)}}\right) \sec{\left(2 a + \frac{\pi}{4} \right)}}{2} + \frac{\sec{\left(2 a \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}}$$
1 cot(a) ---------- + ------------ 2*cot(2*a) 1 - cot(2*a)
$$\frac{1}{2 \cot{\left(2 a \right)}} + \frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}}$$
___
tan(2*a) \/ 2 *(1 + cos(2*a))
-------- - --------------------
2 / pi\
2*cos|2*a + --|
\ 4 /
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{\tan{\left(2 a \right)}}{2}$$
___ / /pi \\
2 \/ 2 *|1 + sin|-- + 2*a||
sin (2*a) \ \2 //
--------- - -------------------------
sin(4*a) / 3*pi\
2*sin|2*a + ----|
\ 4 /
$$- \frac{\sqrt{2} \left(\sin{\left(2 a + \frac{\pi}{2} \right)} + 1\right)}{2 \sin{\left(2 a + \frac{3 \pi}{4} \right)}} + \frac{\sin^{2}{\left(2 a \right)}}{\sin{\left(4 a \right)}}$$
___ 2 2
\/ 2 *cos (a) 2*sin (a)
- ------------- + ----------------------
/ pi\ / 2 \
cos|2*a + --| \1 - tan (a)/*sin(2*a)
\ 4 /
$$- \frac{\sqrt{2} \cos^{2}{\left(a \right)}}{\cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{2 \sin^{2}{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(2 a \right)}}$$
/ 2 \
___ / 2/ pi\\ | -1 + cot (a)|
\/ 2 *|1 + cot |a + --||*|1 + ------------| 2/a\ / 2 \
\ \ 8 // | 2 | 4*cot |-|*\1 + cot (a)/
\ 1 + cot (a) / \2/
- ------------------------------------------- + -----------------------------------
/ 2/ pi\\ 2
2*|-1 + cot |a + --|| / 2/a\\ / 1 \
\ \ 8 // |1 + cot |-|| *|1 - -------|*cot(a)
\ \2// | 2 |
\ cot (a)/
$$- \frac{\sqrt{2} \left(\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} + 1\right) \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} - 1\right)} + \frac{4 \left(\cot^{2}{\left(a \right)} + 1\right) \cot^{2}{\left(\frac{a}{2} \right)}}{\left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \left(\cot^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \cot{\left(a \right)}}$$
/pi \
csc|-- - 2*a|
\2 / csc(a)
------------- + -------------------------------
2*csc(2*a) / csc(2*a) \ /pi \
|1 - -------------|*csc|-- - a|
| /pi \| \2 /
| csc|-- - 2*a||
\ \2 //
$$\frac{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}{2 \csc{\left(2 a \right)}} + \frac{\csc{\left(a \right)}}{\left(- \frac{\csc{\left(2 a \right)}}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- a + \frac{\pi}{2} \right)}}$$
/pi \
csc|-- - a|
\2 / csc(a)
------------------------- + -------------------------------
/ 2/pi \\ / csc(2*a) \ /pi \
| csc |-- - a|| |1 - -------------|*csc|-- - a|
| \2 /| | /pi \| \2 /
|1 - ------------|*csc(a) | csc|-- - 2*a||
| 2 | \ \2 //
\ csc (a) /
$$\frac{\csc{\left(a \right)}}{\left(- \frac{\csc{\left(2 a \right)}}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}} + 1\right) \csc{\left(- a + \frac{\pi}{2} \right)}} + \frac{\csc{\left(- a + \frac{\pi}{2} \right)}}{\left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}}$$
2
___ 2 / pi\ 2*sin (a)
- \/ 2 *cos (a)*sec|2*a + --| + ----------------------
\ 4 / / 2 \
\1 - tan (a)/*sin(2*a)
$$- \sqrt{2} \cos^{2}{\left(a \right)} \sec{\left(2 a + \frac{\pi}{4} \right)} + \frac{2 \sin^{2}{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(2 a \right)}}$$
sin(a) cos(a) -------------------- + --------------------- / 2 \ / cos(2*a)\ | sin (a)| |1 - --------|*sin(a) |1 - -------|*cos(a) \ sin(2*a)/ | 2 | \ cos (a)/
$$\frac{\sin{\left(a \right)}}{\left(- \frac{\sin^{2}{\left(a \right)}}{\cos^{2}{\left(a \right)}} + 1\right) \cos{\left(a \right)}} + \frac{\cos{\left(a \right)}}{\left(1 - \frac{\cos{\left(2 a \right)}}{\sin{\left(2 a \right)}}\right) \sin{\left(a \right)}}$$
/ 2 \
___ / 2/ pi\\ | 1 - tan (a)|
\/ 2 *|1 + tan |a + --||*|1 + -----------|
\ \ 8 // | 2 |
tan(2*a) \ 1 + tan (a)/
-------- - ------------------------------------------
2 / 2/ pi\\
2*|1 - tan |a + --||
\ \ 8 //
$$\frac{\tan{\left(2 a \right)}}{2} - \frac{\sqrt{2} \left(\frac{1 - \tan^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1} + 1\right) \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(a + \frac{\pi}{8} \right)}\right)}$$
tan(a) 1
----------- + ---------------------
2 / 1 \
1 - tan (a) |1 - --------|*tan(a)
\ tan(2*a)/
$$\frac{1}{\left(1 - \frac{1}{\tan{\left(2 a \right)}}\right) \tan{\left(a \right)}} + \frac{\tan{\left(a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
2
___ 2 / pi\ 2*sin (a)*csc(2*a)
- \/ 2 *cos (a)*csc|-2*a + --| + ------------------
\ 4 / 2
1 - tan (a)
$$- \sqrt{2} \cos^{2}{\left(a \right)} \csc{\left(- 2 a + \frac{\pi}{4} \right)} + \frac{2 \sin^{2}{\left(a \right)} \csc{\left(2 a \right)}}{1 - \tan^{2}{\left(a \right)}}$$
tan(2*a) cot(a) -------- + ------------ 2 1 - cot(2*a)
$$\frac{\tan{\left(2 a \right)}}{2} + \frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}}$$
___ / 1 \ / pi\
\/ 2 *|1 + -------------|*csc|-2*a + --|
/pi \ | /pi \| \ 4 /
csc|-- - 2*a| | csc|-- - 2*a||
\2 / \ \2 //
------------- - ----------------------------------------
2*csc(2*a) 2
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}\right) \csc{\left(- 2 a + \frac{\pi}{4} \right)}}{2} + \frac{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}{2 \csc{\left(2 a \right)}}$$
/ pi\ ___ / 1 \ / pi\
2*sec|2*a - --| \/ 2 *|1 + --------|*sec|2*a + --|
\ 2 / \ sec(2*a)/ \ 4 /
------------------------------- - ----------------------------------
/ 2 \ 2
| sec (a) | 2/ pi\
|1 - ------------|*sec |a - --|
| 2/ pi\| \ 2 /
| sec |a - --||
\ \ 2 //
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\sec{\left(2 a \right)}}\right) \sec{\left(2 a + \frac{\pi}{4} \right)}}{2} + \frac{2 \sec{\left(2 a - \frac{\pi}{2} \right)}}{\left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec^{2}{\left(a - \frac{\pi}{2} \right)}}$$
___ 2 / 2/ pi\\
\/ 2 *cos (a)*|1 + tan |a + --||
tan(2*a) \ \ 8 //
-------- - --------------------------------
2 2/ pi\
1 - tan |a + --|
\ 8 /
$$\frac{\tan{\left(2 a \right)}}{2} - \frac{\sqrt{2} \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right) \cos^{2}{\left(a \right)}}{1 - \tan^{2}{\left(a + \frac{\pi}{8} \right)}}$$
___ 2
tan(2*a) \/ 2 *cos (a)
-------- - -------------
2 / pi\
cos|2*a + --|
\ 4 /
$$- \frac{\sqrt{2} \cos^{2}{\left(a \right)}}{\cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{\tan{\left(2 a \right)}}{2}$$
2
sin(2*a) 2*sin (a)
--------------------------- + ------------------------
/ sin(4*a) \ 2 / 4 \
2*|1 - -----------|*sin (a) | 4*sin (a)|
| 2 | |1 - ---------|*sin(2*a)
\ 2*sin (2*a)/ | 2 |
\ sin (2*a)/
$$\frac{2 \sin^{2}{\left(a \right)}}{\left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin{\left(2 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \left(1 - \frac{\sin{\left(4 a \right)}}{2 \sin^{2}{\left(2 a \right)}}\right) \sin^{2}{\left(a \right)}}$$
2 ___
2*sin (a) \/ 2 *(1 + cos(2*a))
---------------------- - --------------------
/ 2 \ / pi\
\1 - tan (a)/*sin(2*a) 2*cos|2*a + --|
\ 4 /
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{2 \sin^{2}{\left(a \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \sin{\left(2 a \right)}}$$
___ 2
tan(2*a) \/ 2 *cos (a)
-------- - --------------------------------
2 / 2/ pi\\ 2/ pi\
|-1 + cot |a + --||*sin |a + --|
\ \ 8 // \ 8 /
$$\frac{\tan{\left(2 a \right)}}{2} - \frac{\sqrt{2} \cos^{2}{\left(a \right)}}{\left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} - 1\right) \sin^{2}{\left(a + \frac{\pi}{8} \right)}}$$
/ pi\
cos|a - --|
\ 2 / cos(a)
------------------------- + -------------------------------
/ 2/ pi\\ / cos(2*a) \ / pi\
| cos |a - --|| |1 - -------------|*cos|a - --|
| \ 2 /| | / pi\| \ 2 /
|1 - ------------|*cos(a) | cos|2*a - --||
| 2 | \ \ 2 //
\ cos (a) /
$$\frac{\cos{\left(a \right)}}{\left(- \frac{\cos{\left(2 a \right)}}{\cos{\left(2 a - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(a - \frac{\pi}{2} \right)}} + \frac{\cos{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos{\left(a \right)}}$$
2/ pi\
2*cos |a - --| ___
\ 2 / \/ 2 *(1 + cos(2*a))
-------------------------------- - --------------------
/ 2/ pi\\ / pi\
| cos |a - --|| 2*cos|2*a + --|
| \ 2 /| / pi\ \ 4 /
|1 - ------------|*cos|2*a - --|
| 2 | \ 2 /
\ cos (a) /
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{2 \cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\cos^{2}{\left(a - \frac{\pi}{2} \right)}}{\cos^{2}{\left(a \right)}}\right) \cos{\left(2 a - \frac{\pi}{2} \right)}}$$
tan(2*a) 1
-------- + ---------------------
2 / 1 \
|1 - --------|*tan(a)
\ tan(2*a)/
$$\frac{\tan{\left(2 a \right)}}{2} + \frac{1}{\left(1 - \frac{1}{\tan{\left(2 a \right)}}\right) \tan{\left(a \right)}}$$
/ pi\
sec|a - --|
sec(a) \ 2 /
------------------------------ + --------------------------
/ 2 \ / / pi\\
| sec (a) | / pi\ | sec|2*a - --||
|1 - ------------|*sec|a - --| | \ 2 /|
| 2/ pi\| \ 2 / |1 - -------------|*sec(a)
| sec |a - --|| \ sec(2*a) /
\ \ 2 //
$$\frac{\sec{\left(a \right)}}{\left(- \frac{\sec^{2}{\left(a \right)}}{\sec^{2}{\left(a - \frac{\pi}{2} \right)}} + 1\right) \sec{\left(a - \frac{\pi}{2} \right)}} + \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\sec{\left(2 a - \frac{\pi}{2} \right)}}{\sec{\left(2 a \right)}}\right) \sec{\left(a \right)}}$$
/ pi\
cos|2*a - --|
\ 2 / cos(a)
------------- + -------------------------------
2*cos(2*a) / cos(2*a) \ / pi\
|1 - -------------|*cos|a - --|
| / pi\| \ 2 /
| cos|2*a - --||
\ \ 2 //
$$\frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(2 a \right)}} + \frac{\cos{\left(a \right)}}{\left(- \frac{\cos{\left(2 a \right)}}{\cos{\left(2 a - \frac{\pi}{2} \right)}} + 1\right) \cos{\left(a - \frac{\pi}{2} \right)}}$$
/ 2 \
___ / 2/ pi\\ | -1 + cot (a)|
\/ 2 *|1 + cot |a + --||*|1 + ------------|
\ \ 8 // | 2 |
1 \ 1 + cot (a) /
---------- - -------------------------------------------
2*cot(2*a) / 2/ pi\\
2*|-1 + cot |a + --||
\ \ 8 //
$$- \frac{\sqrt{2} \left(\frac{\cot^{2}{\left(a \right)} - 1}{\cot^{2}{\left(a \right)} + 1} + 1\right) \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(\cot^{2}{\left(a + \frac{\pi}{8} \right)} - 1\right)} + \frac{1}{2 \cot{\left(2 a \right)}}$$
sec(a) csc(a) -------------------- + --------------------- / 2 \ / csc(2*a)\ | sec (a)| |1 - --------|*sec(a) |1 - -------|*csc(a) \ sec(2*a)/ | 2 | \ csc (a)/
$$\frac{\csc{\left(a \right)}}{\left(- \frac{\csc{\left(2 a \right)}}{\sec{\left(2 a \right)}} + 1\right) \sec{\left(a \right)}} + \frac{\sec{\left(a \right)}}{\left(1 - \frac{\sec^{2}{\left(a \right)}}{\csc^{2}{\left(a \right)}}\right) \csc{\left(a \right)}}$$
tan(2*a) ___ 2 / pi\ -------- - \/ 2 *cos (a)*csc|-2*a + --| 2 \ 4 /
$$- \sqrt{2} \cos^{2}{\left(a \right)} \csc{\left(- 2 a + \frac{\pi}{4} \right)} + \frac{\tan{\left(2 a \right)}}{2}$$
/ 2 \
___ / 2/ pi\\ | 1 - tan (a)|
\/ 2 *|1 + tan |a + --||*|1 + -----------| 2/a\ / 2 \
\ \ 8 // | 2 | 4*tan |-|*\1 + tan (a)/
\ 1 + tan (a)/ \2/
- ------------------------------------------ + -----------------------------------
/ 2/ pi\\ 2
2*|1 - tan |a + --|| / 2/a\\ / 2 \
\ \ 8 // |1 + tan |-|| *\1 - tan (a)/*tan(a)
\ \2//
$$- \frac{\sqrt{2} \left(\frac{1 - \tan^{2}{\left(a \right)}}{\tan^{2}{\left(a \right)} + 1} + 1\right) \left(\tan^{2}{\left(a + \frac{\pi}{8} \right)} + 1\right)}{2 \left(1 - \tan^{2}{\left(a + \frac{\pi}{8} \right)}\right)} + \frac{4 \left(\tan^{2}{\left(a \right)} + 1\right) \tan^{2}{\left(\frac{a}{2} \right)}}{\left(1 - \tan^{2}{\left(a \right)}\right) \left(\tan^{2}{\left(\frac{a}{2} \right)} + 1\right)^{2} \tan{\left(a \right)}}$$
1 cot(a) -------------------- + ------------ / 1 \ 1 - cot(2*a) |1 - -------|*cot(a) | 2 | \ cot (a)/
$$\frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}} + \frac{1}{\left(1 - \frac{1}{\cot^{2}{\left(a \right)}}\right) \cot{\left(a \right)}}$$
2
sin (2*a) sin(2*a)
--------- + ---------------------------
sin(4*a) / sin(4*a) \ 2
2*|1 - -----------|*sin (a)
| 2 |
\ 2*sin (2*a)/
$$\frac{\sin^{2}{\left(2 a \right)}}{\sin{\left(4 a \right)}} + \frac{\sin{\left(2 a \right)}}{2 \left(1 - \frac{\sin{\left(4 a \right)}}{2 \sin^{2}{\left(2 a \right)}}\right) \sin^{2}{\left(a \right)}}$$
___ / /pi \\
2 \/ 2 *|1 + sin|-- + 2*a||
2*sin (a) \ \2 //
------------------------ - -------------------------
/ 4 \ / 3*pi\
| 4*sin (a)| 2*sin|2*a + ----|
|1 - ---------|*sin(2*a) \ 4 /
| 2 |
\ sin (2*a)/
$$- \frac{\sqrt{2} \left(\sin{\left(2 a + \frac{\pi}{2} \right)} + 1\right)}{2 \sin{\left(2 a + \frac{3 \pi}{4} \right)}} + \frac{2 \sin^{2}{\left(a \right)}}{\left(- \frac{4 \sin^{4}{\left(a \right)}}{\sin^{2}{\left(2 a \right)}} + 1\right) \sin{\left(2 a \right)}}$$
tan(2*a) ___ 2 / pi\ -------- - \/ 2 *cos (a)*sec|2*a + --| 2 \ 4 /
$$- \sqrt{2} \cos^{2}{\left(a \right)} \sec{\left(2 a + \frac{\pi}{4} \right)} + \frac{\tan{\left(2 a \right)}}{2}$$
/ pi\
cos|2*a - --| ___
\ 2 / \/ 2 *(1 + cos(2*a))
------------- - --------------------
2*cos(2*a) / pi\
2*cos|2*a + --|
\ 4 /
$$- \frac{\sqrt{2} \left(\cos{\left(2 a \right)} + 1\right)}{2 \cos{\left(2 a + \frac{\pi}{4} \right)}} + \frac{\cos{\left(2 a - \frac{\pi}{2} \right)}}{2 \cos{\left(2 a \right)}}$$
___ / 1 \ / pi\
\/ 2 *|1 + -------------|*csc|-2*a + --|
| /pi \| \ 4 /
| csc|-- - 2*a||
2*csc(2*a) \ \2 //
-------------------------- - ----------------------------------------
/ 2/pi \\ 2
| csc |-- - a||
| \2 /| 2
|1 - ------------|*csc (a)
| 2 |
\ csc (a) /
$$- \frac{\sqrt{2} \left(1 + \frac{1}{\csc{\left(- 2 a + \frac{\pi}{2} \right)}}\right) \csc{\left(- 2 a + \frac{\pi}{4} \right)}}{2} + \frac{2 \csc{\left(2 a \right)}}{\left(1 - \frac{\csc^{2}{\left(- a + \frac{\pi}{2} \right)}}{\csc^{2}{\left(a \right)}}\right) \csc^{2}{\left(a \right)}}$$
/ pi\
sec|a - --|
sec(2*a) \ 2 /
--------------- + --------------------------
/ pi\ / / pi\\
2*sec|2*a - --| | sec|2*a - --||
\ 2 / | \ 2 /|
|1 - -------------|*sec(a)
\ sec(2*a) /
$$\frac{\sec{\left(2 a \right)}}{2 \sec{\left(2 a - \frac{\pi}{2} \right)}} + \frac{\sec{\left(a - \frac{\pi}{2} \right)}}{\left(1 - \frac{\sec{\left(2 a - \frac{\pi}{2} \right)}}{\sec{\left(2 a \right)}}\right) \sec{\left(a \right)}}$$
sec(2*a)/(2*sec(2*a - pi/2)) + sec(a - pi/2)/((1 - sec(2*a - pi/2)/sec(2*a))*sec(a))
Potencias
[src]
/ I*a -I*a\
cot(a) I*\- e + e /
------------ + --------------------------------------
1 - cot(2*a) / 2\
| / I*a -I*a\ |
| \- e + e / | / I*a -I*a\
|1 + -----------------|*\e + e /
| 2 |
| / I*a -I*a\ |
\ \e + e / /
$$\frac{i \left(- e^{i a} + e^{- i a}\right)}{\left(\frac{\left(- e^{i a} + e^{- i a}\right)^{2}}{\left(e^{i a} + e^{- i a}\right)^{2}} + 1\right) \left(e^{i a} + e^{- i a}\right)} + \frac{\cot{\left(a \right)}}{1 - \cot{\left(2 a \right)}}$$
cot(a)/(1 - cot(2*a)) + i*(-exp(i*a) + exp(-i*a))/((1 + (-exp(i*a) + exp(-i*a))^2/(exp(i*a) + exp(-i*a))^2)*(exp(i*a) + exp(-i*a)))
Denominador común
[src]
/ 2 \
-\-cot(a) - tan(a) + tan (a)*cot(a) + cot(2*a)*tan(a)/
-------------------------------------------------------
2 2
1 - tan (a) - cot(2*a) + tan (a)*cot(2*a)
$$- \frac{\tan^{2}{\left(a \right)} \cot{\left(a \right)} + \tan{\left(a \right)} \cot{\left(2 a \right)} - \tan{\left(a \right)} - \cot{\left(a \right)}}{\tan^{2}{\left(a \right)} \cot{\left(2 a \right)} - \tan^{2}{\left(a \right)} - \cot{\left(2 a \right)} + 1}$$
-(-cot(a) - tan(a) + tan(a)^2*cot(a) + cot(2*a)*tan(a))/(1 - tan(a)^2 - cot(2*a) + tan(a)^2*cot(2*a))