Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
-sin(x)/(3*cos(x))+sin(x)/(3*cos(x)^3)
¿Cómo vas a descomponer esta -sin(x)/(3*cos(x))+sin(x)/(3*cos(x)^3) expresión en fracciones?
Solución
Ha introducido
[src]
-sin(x) sin(x)
-------- + ---------
3*cos(x) 3
3*cos (x)
$$\frac{\left(-1\right) \sin{\left(x \right)}}{3 \cos{\left(x \right)}} + \frac{\sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}$$
(-sin(x))/((3*cos(x))) + sin(x)/((3*cos(x)^3))
Respuesta numérica
[src]
0.333333333333333*sin(x)/cos(x)^3 - 0.333333333333333*sin(x)/cos(x)
0.333333333333333*sin(x)/cos(x)^3 - 0.333333333333333*sin(x)/cos(x)
Denominador racional
[src]
3
- 3*cos (x)*sin(x) + 3*cos(x)*sin(x)
------------------------------------
4
9*cos (x)
$$\frac{- 3 \sin{\left(x \right)} \cos^{3}{\left(x \right)} + 3 \sin{\left(x \right)} \cos{\left(x \right)}}{9 \cos^{4}{\left(x \right)}}$$
(-3*cos(x)^3*sin(x) + 3*cos(x)*sin(x))/(9*cos(x)^4)
Denominador común
[src]
/ 2 \
-\-sin(x) + cos (x)*sin(x)/
----------------------------
3
3*cos (x)
$$- \frac{\sin{\left(x \right)} \cos^{2}{\left(x \right)} - \sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}$$
-(-sin(x) + cos(x)^2*sin(x))/(3*cos(x)^3)
Potencias
[src]
/ -I*x I*x\ / -I*x I*x\
I*\- e + e / I*\- e + e /
-------------------- - ------------------
/ I*x -I*x\ 3
|3*e 3*e | / I*x -I*x\
2*|------ + -------| |e e |
\ 2 2 / 6*|---- + -----|
\ 2 2 /
$$\frac{i \left(e^{i x} - e^{- i x}\right)}{2 \left(\frac{3 e^{i x}}{2} + \frac{3 e^{- i x}}{2}\right)} - \frac{i \left(e^{i x} - e^{- i x}\right)}{6 \left(\frac{e^{i x}}{2} + \frac{e^{- i x}}{2}\right)^{3}}$$
sin(x) sin(x)
- -------- + ---------
3*cos(x) 3
3*cos (x)
$$- \frac{\sin{\left(x \right)}}{3 \cos{\left(x \right)}} + \frac{\sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}$$
-sin(x)/(3*cos(x)) + sin(x)/(3*cos(x)^3)
Unión de expresiones racionales
[src]
/ 2 \
\1 - cos (x)/*sin(x)
--------------------
3
3*cos (x)
$$\frac{\left(1 - \cos^{2}{\left(x \right)}\right) \sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}$$
(1 - cos(x)^2)*sin(x)/(3*cos(x)^3)
Combinatoria
[src]
-(1 + cos(x))*(-1 + cos(x))*sin(x)
-----------------------------------
3
3*cos (x)
$$- \frac{\left(\cos{\left(x \right)} - 1\right) \left(\cos{\left(x \right)} + 1\right) \sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}$$
-(1 + cos(x))*(-1 + cos(x))*sin(x)/(3*cos(x)^3)
Compilar la expresión
[src]
sin(x) sin(x)
- -------- + ---------
3*cos(x) 3
3*cos (x)
$$- \frac{\sin{\left(x \right)}}{3 \cos{\left(x \right)}} + \frac{\sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}$$
-sin(x)/(3*cos(x)) + sin(x)/(3*cos(x)^3)
Parte trigonométrica
[src]
sin(x) sin(x)
- -------- + ---------
3*cos(x) 3
3*cos (x)
$$- \frac{\sin{\left(x \right)}}{3 \cos{\left(x \right)}} + \frac{\sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}}$$
/ pi\ /x pi\
cos|x - --| 2*cos|- - --|
\ 2 / \2 2 /
- ----------- + -----------------------------
3*cos(x) 3
/ 2/x pi\\
| cos |- - --||
| \2 2 /| 5/x\
3*|1 - ------------| *cos |-|
| 2/x\ | \2/
| cos |-| |
\ \2/ /
$$- \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{3 \cos{\left(x \right)}} + \frac{2 \cos{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{3 \left(1 - \frac{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} \right)}}\right)^{3} \cos^{5}{\left(\frac{x}{2} \right)}}$$
5/x pi\
2*sec |- - --|
sec(x) \2 2 /
- ------------- + -----------------------------
/ pi\ 3
3*sec|x - --| / 2/x pi\\
\ 2 / | sec |- - --||
| \2 2 /| /x\
3*|-1 + ------------| *sec|-|
| 2/x\ | \2/
| sec |-| |
\ \2/ /
$$- \frac{\sec{\left(x \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{2 \sec^{5}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{3 \left(-1 + \frac{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} \right)}}\right)^{3} \sec{\left(\frac{x}{2} \right)}}$$
tan(x) sin(x)
- ------ + ---------
3 3
3*cos (x)
$$\frac{\sin{\left(x \right)}}{3 \cos^{3}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{3}$$
2
/x\ / 2/x\\ /x\
2*tan|-| 2*|1 + tan |-|| *tan|-|
\2/ \ \2// \2/
- --------------- + -----------------------
/ 2/x\\ 3
3*|1 - tan |-|| / 2/x\\
\ \2// 3*|1 - tan |-||
\ \2//
$$- \frac{2 \tan{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)} + \frac{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \tan{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3}}$$
2
/ 2/x\\ /x\
2*|1 + tan |-|| *tan|-|
tan(x) \ \2// \2/
- ------ + -----------------------
3 3
/ 2/x\\
3*|1 - tan |-||
\ \2//
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \tan{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3}}$$
2
2*sin (x) sin(x)
- ---------- + --------------
3*sin(2*x) 3/ pi\
3*sin |x + --|
\ 2 /
$$- \frac{2 \sin^{2}{\left(x \right)}}{3 \sin{\left(2 x \right)}} + \frac{\sin{\left(x \right)}}{3 \sin^{3}{\left(x + \frac{\pi}{2} \right)}}$$
5/x\ /x\
2*sec |-|*sin|-|
tan(x) \2/ \2/
- ------ + ----------------
3 3
/ 2/x\\
3*|1 - tan |-||
\ \2//
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \sin{\left(\frac{x}{2} \right)} \sec^{5}{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3}}$$
2
/x\ / 2/x\\ /x\
2*cot|-| 2*|1 + cot |-|| *cot|-|
\2/ \ \2// \2/
- ---------------- + -----------------------
/ 2/x\\ 3
3*|-1 + cot |-|| / 2/x\\
\ \2// 3*|-1 + cot |-||
\ \2//
$$- \frac{2 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)} + \frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{3}}$$
/x\
2*tan|-|
tan(x) \2/
- ------ + ---------------------------------------
3 3 4
/ 2/x\\ / 2/x\\ 8/x\
3*|1 - tan |-|| *|1 - tan |-|| *cos |-|
\ \2// \ \4// \4/
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3} \cos^{8}{\left(\frac{x}{4} \right)}}$$
/x\
2*tan|-|
tan(x) \2/
- ------ + ----------------------------------------
3 3 4
/ 2/x\\ / 2/x\\ 8/x\
3*|1 - tan |-|| *|-1 + cot |-|| *sin |-|
\ \2// \ \4// \4/
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4} \sin^{8}{\left(\frac{x}{4} \right)}}$$
5/x\ /x\
2*csc |-|*cos|-|
tan(x) \2/ \2/
- ------ + -----------------
3 3
/ 1 \
3*|-1 + -------|
| 2/x\|
| tan |-||
\ \2//
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \cos{\left(\frac{x}{2} \right)} \csc^{5}{\left(\frac{x}{2} \right)}}{3 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{3}}$$
tan(x) 4*sin(x)
- ------ + -----------------------
3 3*(3*cos(x) + cos(3*x))
$$- \frac{\tan{\left(x \right)}}{3} + \frac{4 \sin{\left(x \right)}}{3 \left(3 \cos{\left(x \right)} + \cos{\left(3 x \right)}\right)}$$
4
/ 2/x\\
|1 + tan |-||
tan(x) \ \4//
- ------ + ---------------------------------
3 3
/ 1 \ /x\ 4/x\
24*|-1 + -------| *tan|-|*tan |-|
| 2/x\| \2/ \4/
| tan |-||
\ \2//
$$- \frac{\tan{\left(x \right)}}{3} + \frac{\left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}}{24 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{3} \tan^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}$$
3 sec(x) sec (x) - -------- + -------- 3*csc(x) 3*csc(x)
$$\frac{\sec^{3}{\left(x \right)}}{3 \csc{\left(x \right)}} - \frac{\sec{\left(x \right)}}{3 \csc{\left(x \right)}}$$
2
/ 2/x\\ /x\
2*|1 + cot |-|| *cot|-|
1 \ \2// \2/
- -------- + -----------------------
3*cot(x) 3
/ 2/x\\
3*|-1 + cot |-||
\ \2//
$$- \frac{1}{3 \cot{\left(x \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)^{2} \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{3}}$$
/x\
2*tan|-|
tan(x) \2/
- ------ + ------------------------
3 3
/ 2/x\\ 4/x\
3*|1 - tan |-|| *cos |-|
\ \2// \2/
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \tan{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3} \cos^{4}{\left(\frac{x}{2} \right)}}$$
/x\
2*cot|-|
tan(x) \2/
- ------ + -------------------------
3 3
/ 2/x\\ 4/x\
3*|-1 + cot |-|| *sin |-|
\ \2// \2/
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \cot{\left(\frac{x}{2} \right)}}{3 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{3} \sin^{4}{\left(\frac{x}{2} \right)}}$$
4/x\ /x\
tan |-|*cot|-|
tan(x) \4/ \2/
- ------ + --------------------------
3 3
/ 2/x\\ 8/x\
24*|-1 + cot |-|| *sin |-|
\ \2// \4/
$$- \frac{\tan{\left(x \right)}}{3} + \frac{\tan^{4}{\left(\frac{x}{4} \right)} \cot{\left(\frac{x}{2} \right)}}{24 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{3} \sin^{8}{\left(\frac{x}{4} \right)}}$$
2
2*sin (x) sin(x)
- ---------- + ---------------------------
3*sin(2*x) 3
/ 2 \
| sin (x) | 6/x\
3*|-1 + ---------| *sin |-|
| 4/x\| \2/
| 4*sin |-||
\ \2//
$$- \frac{2 \sin^{2}{\left(x \right)}}{3 \sin{\left(2 x \right)}} + \frac{\sin{\left(x \right)}}{3 \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right)^{3} \sin^{6}{\left(\frac{x}{2} \right)}}$$
/ pi\ / pi\
cos|x - --| cos|x - --|
\ 2 / \ 2 /
- ----------- + -----------
3*cos(x) 3
3*cos (x)
$$- \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{3 \cos{\left(x \right)}} + \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{3 \cos^{3}{\left(x \right)}}$$
4
/ 2/x\\ /x\
2*|1 + tan |-|| *tan|-|
tan(x) \ \4// \2/
- ------ + -------------------------------
3 3 4
/ 2/x\\ / 2/x\\
3*|1 - tan |-|| *|1 - tan |-||
\ \2// \ \4//
$$- \frac{\tan{\left(x \right)}}{3} + \frac{2 \left(\tan^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4} \tan{\left(\frac{x}{2} \right)}}{3 \left(1 - \tan^{2}{\left(\frac{x}{4} \right)}\right)^{4} \left(1 - \tan^{2}{\left(\frac{x}{2} \right)}\right)^{3}}$$
3 /x\
(-1 + cos(x)) *cos|-|
tan(x) \2/
- ------ - ---------------------
3 3 5/x\
12*cos (x)*sin |-|
\2/
$$- \frac{\left(\cos{\left(x \right)} - 1\right)^{3} \cos{\left(\frac{x}{2} \right)}}{12 \sin^{5}{\left(\frac{x}{2} \right)} \cos^{3}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{3}$$
tan(x) sin(x)
- ------ + ---------------------------
3 3
/ 2 \
| sin (x) | 6/x\
3*|-1 + ---------| *sin |-|
| 4/x\| \2/
| 4*sin |-||
\ \2//
$$- \frac{\tan{\left(x \right)}}{3} + \frac{\sin{\left(x \right)}}{3 \left(-1 + \frac{\sin^{2}{\left(x \right)}}{4 \sin^{4}{\left(\frac{x}{2} \right)}}\right)^{3} \sin^{6}{\left(\frac{x}{2} \right)}}$$
4
/ 2/x\\
2*|1 + cot |-||
1 \ \4//
- -------- + ---------------------------------------
3*cot(x) 3 4
/ 1 \ / 2/x\\ /x\
3*|1 - -------| *|-1 + cot |-|| *cot|-|
| 2/x\| \ \4// \2/
| cot |-||
\ \2//
$$- \frac{1}{3 \cot{\left(x \right)}} + \frac{2 \left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4}}{3 \left(1 - \frac{1}{\cot^{2}{\left(\frac{x}{2} \right)}}\right)^{3} \left(\cot^{2}{\left(\frac{x}{4} \right)} - 1\right)^{4} \cot{\left(\frac{x}{2} \right)}}$$
/pi \ 3/pi \
csc|-- - x| csc |-- - x|
\2 / \2 /
- ----------- + ------------
3*csc(x) 3*csc(x)
$$\frac{\csc^{3}{\left(- x + \frac{\pi}{2} \right)}}{3 \csc{\left(x \right)}} - \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{3 \csc{\left(x \right)}}$$
/ pi\ /x\
cos|x - --| 2*cos|-|
\ 2 / \2/
- ----------- + -----------------------------------
3*cos(x) 3
/ 2/x\ \
| cos |-| |
| \2/ | 5/x pi\
3*|-1 + ------------| *cos |- - --|
| 2/x pi\| \2 2 /
| cos |- - --||
\ \2 2 //
$$- \frac{\cos{\left(x - \frac{\pi}{2} \right)}}{3 \cos{\left(x \right)}} + \frac{2 \cos{\left(\frac{x}{2} \right)}}{3 \left(\frac{\cos^{2}{\left(\frac{x}{2} \right)}}{\cos^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} - 1\right)^{3} \cos^{5}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$
5/x\
2*sec |-|
sec(x) \2/
- ------------- + ---------------------------------
/ pi\ 3
3*sec|x - --| / 2/x\ \
\ 2 / | sec |-| |
| \2/ | /x pi\
3*|1 - ------------| *sec|- - --|
| 2/x pi\| \2 2 /
| sec |- - --||
\ \2 2 //
$$- \frac{\sec{\left(x \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{2 \sec^{5}{\left(\frac{x}{2} \right)}}{3 \left(- \frac{\sec^{2}{\left(\frac{x}{2} \right)}}{\sec^{2}{\left(\frac{x}{2} - \frac{\pi}{2} \right)}} + 1\right)^{3} \sec{\left(\frac{x}{2} - \frac{\pi}{2} \right)}}$$
/pi \ 5/pi x\
csc|-- - x| 2*csc |-- - -|
\2 / \2 2/
- ----------- + ----------------------------
3*csc(x) 3
/ 2/pi x\\
| csc |-- - -||
| \2 2/| /x\
3*|1 - ------------| *csc|-|
| 2/x\ | \2/
| csc |-| |
\ \2/ /
$$- \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{3 \csc{\left(x \right)}} + \frac{2 \csc^{5}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{3 \left(1 - \frac{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}{\csc^{2}{\left(\frac{x}{2} \right)}}\right)^{3} \csc{\left(\frac{x}{2} \right)}}$$
tan(x) 1
- ------ + -----------------------------------------
3 3
/ 1 \ 8/x\ /x\ 4/x\
24*|-1 + -------| *cos |-|*tan|-|*tan |-|
| 2/x\| \4/ \2/ \4/
| tan |-||
\ \2//
$$- \frac{\tan{\left(x \right)}}{3} + \frac{1}{24 \left(-1 + \frac{1}{\tan^{2}{\left(\frac{x}{2} \right)}}\right)^{3} \cos^{8}{\left(\frac{x}{4} \right)} \tan^{4}{\left(\frac{x}{4} \right)} \tan{\left(\frac{x}{2} \right)}}$$
2/x\
2 4*sin |-|
2*sin (x) \2/
- ---------- + --------------------------------------
3*sin(2*x) 3
/ 4/x\\
| 4*sin |-||
| \2/| 4/pi x\
3*|1 - ---------| *sin(x)*sin |-- + -|
| 2 | \2 2/
\ sin (x) /
$$- \frac{2 \sin^{2}{\left(x \right)}}{3 \sin{\left(2 x \right)}} + \frac{4 \sin^{2}{\left(\frac{x}{2} \right)}}{3 \left(- \frac{4 \sin^{4}{\left(\frac{x}{2} \right)}}{\sin^{2}{\left(x \right)}} + 1\right)^{3} \sin{\left(x \right)} \sin^{4}{\left(\frac{x}{2} + \frac{\pi}{2} \right)}}$$
4
/ 2/x\\ /x\
|1 + cot |-|| *cot|-|
1 \ \4// \2/
- -------- + --------------------------
3*cot(x) 3
/ 2/x\\ 4/x\
24*|-1 + cot |-|| *cot |-|
\ \2// \4/
$$\frac{\left(\cot^{2}{\left(\frac{x}{4} \right)} + 1\right)^{4} \cot{\left(\frac{x}{2} \right)}}{24 \left(\cot^{2}{\left(\frac{x}{2} \right)} - 1\right)^{3} \cot^{4}{\left(\frac{x}{4} \right)}} - \frac{1}{3 \cot{\left(x \right)}}$$
sin(x) sin(x)
- ------------- + --------------
/ pi\ 3/ pi\
3*sin|x + --| 3*sin |x + --|
\ 2 / \ 2 /
$$- \frac{\sin{\left(x \right)}}{3 \sin{\left(x + \frac{\pi}{2} \right)}} + \frac{\sin{\left(x \right)}}{3 \sin^{3}{\left(x + \frac{\pi}{2} \right)}}$$
3
sec(x) sec (x)
- ------------- + -------------
/ pi\ / pi\
3*sec|x - --| 3*sec|x - --|
\ 2 / \ 2 /
$$\frac{\sec^{3}{\left(x \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}} - \frac{\sec{\left(x \right)}}{3 \sec{\left(x - \frac{\pi}{2} \right)}}$$
/pi \ 5/x\
csc|-- - x| 2*csc |-|
\2 / \2/
- ----------- + ----------------------------------
3*csc(x) 3
/ 2/x\ \
| csc |-| |
| \2/ | /pi x\
3*|-1 + ------------| *csc|-- - -|
| 2/pi x\| \2 2/
| csc |-- - -||
\ \2 2//
$$- \frac{\csc{\left(- x + \frac{\pi}{2} \right)}}{3 \csc{\left(x \right)}} + \frac{2 \csc^{5}{\left(\frac{x}{2} \right)}}{3 \left(\frac{\csc^{2}{\left(\frac{x}{2} \right)}}{\csc^{2}{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}} - 1\right)^{3} \csc{\left(- \frac{x}{2} + \frac{\pi}{2} \right)}}$$
3 /x\
(1 + cos(x)) *sin|-|
tan(x) \2/
- ------ + --------------------
3 3 5/x\
12*cos (x)*cos |-|
\2/
$$\frac{\left(\cos{\left(x \right)} + 1\right)^{3} \sin{\left(\frac{x}{2} \right)}}{12 \cos^{5}{\left(\frac{x}{2} \right)} \cos^{3}{\left(x \right)}} - \frac{\tan{\left(x \right)}}{3}$$
-tan(x)/3 + (1 + cos(x))^3*sin(x/2)/(12*cos(x)^3*cos(x/2)^5)