Sr Examen
Simplificación de expresiones/
Descomposición en fracciones simples/
sin(t)*cot(t)/((cos(t)*tan(t)))
¿Cómo vas a descomponer esta sin(t)*cot(t)/((cos(t)*tan(t))) expresión en fracciones?
Solución
Ha introducido
[src]
sin(t)*cot(t) ------------- cos(t)*tan(t)
$$\frac{\sin{\left(t \right)} \cot{\left(t \right)}}{\cos{\left(t \right)} \tan{\left(t \right)}}$$
(sin(t)*cot(t))/((cos(t)*tan(t)))
Potencias
[src]
/ -I*t I*t\ / I*t -I*t\
-\- e + e /*\e + e /*cot(t)
----------------------------------------
/ I*t -I*t\
|e e | / I*t -I*t\
2*|---- + -----|*\- e + e /
\ 2 2 /
$$- \frac{\left(e^{i t} - e^{- i t}\right) \left(e^{i t} + e^{- i t}\right) \cot{\left(t \right)}}{2 \left(- e^{i t} + e^{- i t}\right) \left(\frac{e^{i t}}{2} + \frac{e^{- i t}}{2}\right)}$$
-(-exp(-i*t) + exp(i*t))*(exp(i*t) + exp(-i*t))*cot(t)/(2*(exp(i*t)/2 + exp(-i*t)/2)*(-exp(i*t) + exp(-i*t)))
Parte trigonométrica
[src]
1 cos(2*t) ------------- + ------------- / pi\ / pi\ cos|2*t - --| cos|2*t - --| \ 2 / \ 2 /
$$\frac{\cos{\left(2 t \right)}}{\cos{\left(2 t - \frac{\pi}{2} \right)}} + \frac{1}{\cos{\left(2 t - \frac{\pi}{2} \right)}}$$
2 1 + cot (t) ----------- + cot(2*t) 2*cot(t)
$$\frac{\cot^{2}{\left(t \right)} + 1}{2 \cot{\left(t \right)}} + \cot{\left(2 t \right)}$$
1 1 -------- + -------- sin(2*t) tan(2*t)
$$\frac{1}{\tan{\left(2 t \right)}} + \frac{1}{\sin{\left(2 t \right)}}$$
csc(t) ----------- /pi \ csc|-- - t| \2 /
$$\frac{\csc{\left(t \right)}}{\csc{\left(- t + \frac{\pi}{2} \right)}}$$
1 sin(4*t)
-------- + -----------
sin(2*t) 2
2*sin (2*t)
$$\frac{1}{\sin{\left(2 t \right)}} + \frac{\sin{\left(4 t \right)}}{2 \sin^{2}{\left(2 t \right)}}$$
2
sin (2*t)
----------------
3
4*cos(t)*sin (t)
$$\frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{3}{\left(t \right)} \cos{\left(t \right)}}$$
/ pi\ sec|2*t - --| \ 2 / / pi\ ------------- + sec|2*t - --| sec(2*t) \ 2 /
$$\sec{\left(2 t - \frac{\pi}{2} \right)} + \frac{\sec{\left(2 t - \frac{\pi}{2} \right)}}{\sec{\left(2 t \right)}}$$
cot(t)
$$\cot{\left(t \right)}$$
2 /t\
2*cot (t)*cot|-|
\2/
----------------
2/t\
-1 + cot |-|
\2/
$$\frac{2 \cot{\left(\frac{t}{2} \right)} \cot^{2}{\left(t \right)}}{\cot^{2}{\left(\frac{t}{2} \right)} - 1}$$
/ pi\ sec|t - --| \ 2 / ----------- sec(t)
$$\frac{\sec{\left(t - \frac{\pi}{2} \right)}}{\sec{\left(t \right)}}$$
csc(t) ------ sec(t)
$$\frac{\csc{\left(t \right)}}{\sec{\left(t \right)}}$$
cos(t) ----------- / pi\ cos|t - --| \ 2 /
$$\frac{\cos{\left(t \right)}}{\cos{\left(t - \frac{\pi}{2} \right)}}$$
1 -------- + csc(2*t) tan(2*t)
$$\csc{\left(2 t \right)} + \frac{1}{\tan{\left(2 t \right)}}$$
1 ------ tan(t)
$$\frac{1}{\tan{\left(t \right)}}$$
/t\
2*tan|-|
\2/
---------------------
/ 2/t\\ 2
|1 - tan |-||*tan (t)
\ \2//
$$\frac{2 \tan{\left(\frac{t}{2} \right)}}{\left(1 - \tan^{2}{\left(\frac{t}{2} \right)}\right) \tan^{2}{\left(t \right)}}$$
sin(2*t)
---------
2
2*sin (t)
$$\frac{\sin{\left(2 t \right)}}{2 \sin^{2}{\left(t \right)}}$$
cos(t) ------ sin(t)
$$\frac{\cos{\left(t \right)}}{\sin{\left(t \right)}}$$
csc(2*t) ------------- + csc(2*t) /pi \ csc|-- - 2*t| \2 /
$$\csc{\left(2 t \right)} + \frac{\csc{\left(2 t \right)}}{\csc{\left(- 2 t + \frac{\pi}{2} \right)}}$$
2
sin (2*t)
---------------------
3 / pi\
4*sin (t)*sin|t + --|
\ 2 /
$$\frac{\sin^{2}{\left(2 t \right)}}{4 \sin^{3}{\left(t \right)} \sin{\left(t + \frac{\pi}{2} \right)}}$$
2 1 1 + tan (t) -------- + ----------- tan(2*t) 2*tan(t)
$$\frac{\tan^{2}{\left(t \right)} + 1}{2 \tan{\left(t \right)}} + \frac{1}{\tan{\left(2 t \right)}}$$
1/tan(2*t) + (1 + tan(t)^2)/(2*tan(t))