Álgebra Ejemplos

$\frac{\csc (x) \cos (x)}{\tan (x) + \cot (x)}$

Paso 1

Reescribe $\csc (x)$ en términos de senos y cosenos.

$\frac{\frac{1}{\sin (x)} \cos (x)}{\tan (x) + \cot (x)}$

Paso 2

Simplifica el denominador.

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Paso 2.1

Reescribe $\tan (x)$ en términos de senos y cosenos.

$\frac{\frac{1}{\sin (x)} \cos (x)}{\frac{\sin (x)}{\cos (x)} + \cot (x)}$

Paso 2.2

Reescribe $\cot (x)$ en términos de senos y cosenos.

$\frac{\frac{1}{\sin (x)} \cos (x)}{\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)}}$

Paso 3

Combina $\frac{1}{\sin (x)}$ y $\cos (x)$ .

$\frac{\frac{\cos (x)}{\sin (x)}}{\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)}}$

Paso 4

Multiplica el numerador por la recíproca del denominador.

$\frac{\cos (x)}{\sin (x)} \cdot \frac{1}{\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)}}$

Paso 5

Multiplica $\frac{\cos (x)}{\sin (x)}$ por $\frac{1}{\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)}}$ .

$\frac{\cos (x)}{\sin (x) (\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)})}$

Paso 6

Separa las fracciones.

$\frac{1}{\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)}} \cdot \frac{\cos (x)}{\sin (x)}$

Paso 7

Convierte de $\frac{\cos (x)}{\sin (x)}$ a $\cot (x)$ .

$\frac{1}{\frac{\sin (x)}{\cos (x)} + \frac{\cos (x)}{\sin (x)}} \cot (x)$

Paso 8

Simplifica cada término.

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Paso 8.1

Convierte de $\frac{\sin (x)}{\cos (x)}$ a $\tan (x)$ .

$\frac{1}{\tan (x) + \frac{\cos (x)}{\sin (x)}} \cot (x)$

Paso 8.2

Convierte de $\frac{\cos (x)}{\sin (x)}$ a $\cot (x)$ .

$\frac{1}{\tan (x) + \cot (x)} \cot (x)$

Paso 9

Combina $\frac{1}{\tan (x) + \cot (x)}$ y $\cot (x)$ .

$\frac{\cot (x)}{\tan (x) + \cot (x)}$