Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
cos(x)+t*sin(x)/(1-t*(x^2)/2)*x
¿Cómo vas a descomponer esta cos(x)+t*sin(x)/(1-t*(x^2)/2)*x expresión en fracciones?
Solución
Ha introducido
[src]
t*sin(x)
cos(x) + --------*x
2
t*x
1 - ----
2
$$x \frac{t \sin{\left(x \right)}}{- \frac{t x^{2}}{2} + 1} + \cos{\left(x \right)}$$
cos(x) + ((t*sin(x))/(1 - t*x^2/2))*x
Simplificación general
[src]
/ 2\
\-2 + t*x /*cos(x) - 2*t*x*sin(x)
---------------------------------
2
-2 + t*x
$$\frac{- 2 t x \sin{\left(x \right)} + \left(t x^{2} - 2\right) \cos{\left(x \right)}}{t x^{2} - 2}$$
((-2 + t*x^2)*cos(x) - 2*t*x*sin(x))/(-2 + t*x^2)
Respuesta numérica
[src]
t*x*sin(x)/(1.0 - 0.5*t*x^2) + cos(x)
t*x*sin(x)/(1.0 - 0.5*t*x^2) + cos(x)
Denominador racional
[src]
/ 2\
\2 - t*x /*cos(x) + 2*t*x*sin(x)
--------------------------------
2
2 - t*x
$$\frac{2 t x \sin{\left(x \right)} + \left(- t x^{2} + 2\right) \cos{\left(x \right)}}{- t x^{2} + 2}$$
((2 - t*x^2)*cos(x) + 2*t*x*sin(x))/(2 - t*x^2)
Combinatoria
[src]
2
-2*cos(x) + t*x *cos(x) - 2*t*x*sin(x)
--------------------------------------
2
-2 + t*x
$$\frac{t x^{2} \cos{\left(x \right)} - 2 t x \sin{\left(x \right)} - 2 \cos{\left(x \right)}}{t x^{2} - 2}$$
(-2*cos(x) + t*x^2*cos(x) - 2*t*x*sin(x))/(-2 + t*x^2)
Potencias
[src]
t*x*sin(x)
---------- + cos(x)
2
t*x
1 - ----
2
$$\frac{t x \sin{\left(x \right)}}{- \frac{t x^{2}}{2} + 1} + \cos{\left(x \right)}$$
I*x -I*x / -I*x I*x\
e e I*t*x*\- e + e /
---- + ----- - ----------------------
2 2 / 2\
| t*x |
2*|1 - ----|
\ 2 /
$$- \frac{i t x \left(e^{i x} - e^{- i x}\right)}{2 \left(- \frac{t x^{2}}{2} + 1\right)} + \frac{e^{i x}}{2} + \frac{e^{- i x}}{2}$$
exp(i*x)/2 + exp(-i*x)/2 - i*t*x*(-exp(-i*x) + exp(i*x))/(2*(1 - t*x^2/2))
Unión de expresiones racionales
[src]
/ 2\
\2 - t*x /*cos(x) + 2*t*x*sin(x)
--------------------------------
2
2 - t*x
$$\frac{2 t x \sin{\left(x \right)} + \left(- t x^{2} + 2\right) \cos{\left(x \right)}}{- t x^{2} + 2}$$
((2 - t*x^2)*cos(x) + 2*t*x*sin(x))/(2 - t*x^2)
Denominador común
[src]
2*t*x*sin(x)
- ------------ + cos(x)
2
-2 + t*x
$$- \frac{2 t x \sin{\left(x \right)}}{t x^{2} - 2} + \cos{\left(x \right)}$$
-2*t*x*sin(x)/(-2 + t*x^2) + cos(x)
Compilar la expresión
[src]
t*x*sin(x)
---------- + cos(x)
2
t*x
1 - ----
2
$$\frac{t x \sin{\left(x \right)}}{- \frac{t x^{2}}{2} + 1} + \cos{\left(x \right)}$$
t*x*sin(x)/(1 - t*x^2/2) + cos(x)
Parte trigonométrica
[src]
2/x\ /x\
-1 + cot |-| 2*t*x*cot|-|
\2/ \2/
------------ + ------------------------
2/x\ / 2\
1 + cot |-| / 2/x\\ | t*x |
\2/ |1 + cot |-||*|1 - ----|
\ \2// \ 2 /
$$\frac{2 t x \cot{\left(\frac{x}{2} \right)}}{\left(- \frac{t x^{2}}{2} + 1\right) \left(\cot^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{\cot^{2}{\left(\frac{x}{2} \right)} - 1}{\cot^{2}{\left(\frac{x}{2} \right)} + 1}$$
t*x*sin(x) / pi\
---------- + sin|x + --|
2 \ 2 /
t*x
1 - ----
2
$$\frac{t x \sin{\left(x \right)}}{- \frac{t x^{2}}{2} + 1} + \sin{\left(x + \frac{\pi}{2} \right)}$$
2/x\ /x\
1 - tan |-| 2*t*x*tan|-|
\2/ \2/
----------- + ------------------------
2/x\ / 2\
1 + tan |-| / 2/x\\ | t*x |
\2/ |1 + tan |-||*|1 - ----|
\ \2// \ 2 /
$$\frac{2 t x \tan{\left(\frac{x}{2} \right)}}{\left(- \frac{t x^{2}}{2} + 1\right) \left(\tan^{2}{\left(\frac{x}{2} \right)} + 1\right)} + \frac{1 - \tan^{2}{\left(\frac{x}{2} \right)}}{\tan^{2}{\left(\frac{x}{2} \right)} + 1}$$
/ pi\
t*x*cos|x - --|
\ 2 /
--------------- + cos(x)
2
t*x
1 - ----
2
$$\frac{t x \cos{\left(x - \frac{\pi}{2} \right)}}{- \frac{t x^{2}}{2} + 1} + \cos{\left(x \right)}$$
1 t*x
------ + -----------------
sec(x) / 2\
| t*x |
|1 - ----|*csc(x)
\ 2 /
$$\frac{t x}{\left(- \frac{t x^{2}}{2} + 1\right) \csc{\left(x \right)}} + \frac{1}{\sec{\left(x \right)}}$$
1 t*x
----------- + -----------------
/pi \ / 2\
csc|-- - x| | t*x |
\2 / |1 - ----|*csc(x)
\ 2 /
$$\frac{t x}{\left(- \frac{t x^{2}}{2} + 1\right) \csc{\left(x \right)}} + \frac{1}{\csc{\left(- x + \frac{\pi}{2} \right)}}$$
t*x*sin(x)
---------- + cos(x)
2
t*x
1 - ----
2
$$\frac{t x \sin{\left(x \right)}}{- \frac{t x^{2}}{2} + 1} + \cos{\left(x \right)}$$
1 t*x
------ + ----------------------
sec(x) / 2\
| t*x | / pi\
|1 - ----|*sec|x - --|
\ 2 / \ 2 /
$$\frac{t x}{\left(- \frac{t x^{2}}{2} + 1\right) \sec{\left(x - \frac{\pi}{2} \right)}} + \frac{1}{\sec{\left(x \right)}}$$
1/sec(x) + t*x/((1 - t*x^2/2)*sec(x - pi/2))