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