Sr Examen
¿Cómo vas a descomponer esta sin(2nx)/(2n)-cos(2nx)/(4n^2) expresión en fracciones?
Solución
Ha introducido
[src]
sin(2*n*x) cos(2*n*x)
---------- - ----------
2*n 2
4*n
$$- \frac{\cos{\left(2 n x \right)}}{4 n^{2}} + \frac{\sin{\left(2 n x \right)}}{2 n}$$
sin((2*n)*x)/((2*n)) - cos((2*n)*x)/(4*n^2)
Simplificación general
[src]
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
2
4*n
$$\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}}$$
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Respuesta numérica
[src]
0.5*sin((2*n)*x)/n - 0.25*cos((2*n)*x)/n^2
0.5*sin((2*n)*x)/n - 0.25*cos((2*n)*x)/n^2
Denominador racional
[src]
2
-2*n*cos(2*n*x) + 4*n *sin(2*n*x)
---------------------------------
3
8*n
$$\frac{4 n^{2} \sin{\left(2 n x \right)} - 2 n \cos{\left(2 n x \right)}}{8 n^{3}}$$
(-2*n*cos(2*n*x) + 4*n^2*sin(2*n*x))/(8*n^3)
Combinatoria
[src]
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
2
4*n
$$\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}}$$
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Potencias
[src]
-2*I*n*x 2*I*n*x
e e
--------- + -------- / -2*I*n*x 2*I*n*x\
2 2 I*\- e + e /
- -------------------- - --------------------------
2 4*n
4*n
$$- \frac{i \left(e^{2 i n x} - e^{- 2 i n x}\right)}{4 n} - \frac{\frac{e^{2 i n x}}{2} + \frac{e^{- 2 i n x}}{2}}{4 n^{2}}$$
sin(2*n*x) cos(2*n*x)
---------- - ----------
2*n 2
4*n
$$\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}}$$
sin(2*n*x)/(2*n) - cos(2*n*x)/(4*n^2)
Denominador común
[src]
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
2
4*n
$$\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}}$$
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Unión de expresiones racionales
[src]
-cos(2*n*x) + 2*n*sin(2*n*x)
----------------------------
2
4*n
$$\frac{2 n \sin{\left(2 n x \right)} - \cos{\left(2 n x \right)}}{4 n^{2}}$$
(-cos(2*n*x) + 2*n*sin(2*n*x))/(4*n^2)
Compilar la expresión
[src]
sin(2*n*x) cos(2*n*x)
---------- - ----------
2*n 2
4*n
$$\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}}$$
sin((2*n)*x)/(2*n) - cos((2*n)*x)/(4*n^2)
Parte trigonométrica
[src]
1 1
-------------- - --------------------
2*n*csc(2*n*x) 2 /pi \
4*n *csc|-- - 2*n*x|
\2 /
$$\frac{1}{2 n \csc{\left(2 n x \right)}} - \frac{1}{4 n^{2} \csc{\left(- 2 n x + \frac{\pi}{2} \right)}}$$
/ pi \ cos(2*n*x)
2*cos|- -- + 2*n*x| - ----------
\ 2 / n
--------------------------------
4*n
$$\frac{2 \cos{\left(2 n x - \frac{\pi}{2} \right)} - \frac{\cos{\left(2 n x \right)}}{n}}{4 n}$$
2 1
----------------- - ------------
/ pi \ n*sec(2*n*x)
sec|- -- + 2*n*x|
\ 2 /
--------------------------------
4*n
$$\frac{\frac{2}{\sec{\left(2 n x - \frac{\pi}{2} \right)}} - \frac{1}{n \sec{\left(2 n x \right)}}}{4 n}$$
2
4*cot(n*x) -1 + cot (n*x)
------------- - -----------------
2 / 2 \
1 + cot (n*x) n*\1 + cot (n*x)/
---------------------------------
4*n
$$\frac{\frac{4 \cot{\left(n x \right)}}{\cot^{2}{\left(n x \right)} + 1} - \frac{\cot^{2}{\left(n x \right)} - 1}{n \left(\cot^{2}{\left(n x \right)} + 1\right)}}{4 n}$$
1 1
--------------------- - ---------------
/ pi \ 2
2*n*sec|- -- + 2*n*x| 4*n *sec(2*n*x)
\ 2 /
$$\frac{1}{2 n \sec{\left(2 n x - \frac{\pi}{2} \right)}} - \frac{1}{4 n^{2} \sec{\left(2 n x \right)}}$$
/pi \
sin|-- + 2*n*x|
\2 /
2*sin(2*n*x) - ---------------
n
------------------------------
4*n
$$\frac{2 \sin{\left(2 n x \right)} - \frac{\sin{\left(2 n x + \frac{\pi}{2} \right)}}{n}}{4 n}$$
/pi \
sin|-- + 2*n*x|
sin(2*n*x) \2 /
---------- - ---------------
2*n 2
4*n
$$\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\sin{\left(2 n x + \frac{\pi}{2} \right)}}{4 n^{2}}$$
1 1
-------------- - ---------------
2*n*csc(2*n*x) 2
4*n *sec(2*n*x)
$$\frac{1}{2 n \csc{\left(2 n x \right)}} - \frac{1}{4 n^{2} \sec{\left(2 n x \right)}}$$
2
4*tan(n*x) 1 - tan (n*x)
------------- - -----------------
2 / 2 \
1 + tan (n*x) n*\1 + tan (n*x)/
---------------------------------
4*n
$$\frac{\frac{4 \tan{\left(n x \right)}}{\tan^{2}{\left(n x \right)} + 1} - \frac{1 - \tan^{2}{\left(n x \right)}}{n \left(\tan^{2}{\left(n x \right)} + 1\right)}}{4 n}$$
sin(2*n*x) cos(2*n*x)
---------- - ----------
2*n 2
4*n
$$\frac{\sin{\left(2 n x \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}}$$
cos(2*n*x)
2*sin(2*n*x) - ----------
n
-------------------------
4*n
$$\frac{2 \sin{\left(2 n x \right)} - \frac{\cos{\left(2 n x \right)}}{n}}{4 n}$$
2
tan(n*x) 1 - tan (n*x)
----------------- - --------------------
/ 2 \ 2 / 2 \
n*\1 + tan (n*x)/ 4*n *\1 + tan (n*x)/
$$\frac{\tan{\left(n x \right)}}{n \left(\tan^{2}{\left(n x \right)} + 1\right)} - \frac{1 - \tan^{2}{\left(n x \right)}}{4 n^{2} \left(\tan^{2}{\left(n x \right)} + 1\right)}$$
/ pi \
cos|- -- + 2*n*x|
\ 2 / cos(2*n*x)
----------------- - ----------
2*n 2
4*n
$$\frac{\cos{\left(2 n x - \frac{\pi}{2} \right)}}{2 n} - \frac{\cos{\left(2 n x \right)}}{4 n^{2}}$$
2 1
---------- - -----------------
csc(2*n*x) /pi \
n*csc|-- - 2*n*x|
\2 /
------------------------------
4*n
$$\frac{\frac{2}{\csc{\left(2 n x \right)}} - \frac{1}{n \csc{\left(- 2 n x + \frac{\pi}{2} \right)}}}{4 n}$$
2
cot(n*x) -1 + cot (n*x)
----------------- - --------------------
/ 2 \ 2 / 2 \
n*\1 + cot (n*x)/ 4*n *\1 + cot (n*x)/
$$\frac{\cot{\left(n x \right)}}{n \left(\cot^{2}{\left(n x \right)} + 1\right)} - \frac{\cot^{2}{\left(n x \right)} - 1}{4 n^{2} \left(\cot^{2}{\left(n x \right)} + 1\right)}$$
cot(n*x)/(n*(1 + cot(n*x)^2)) - (-1 + cot(n*x)^2)/(4*n^2*(1 + cot(n*x)^2))