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