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