Álgebra Ejemplos

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

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

Paso 1

Reescribe

\csc (x)

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

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

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

Paso 2

Simplifica el denominador.

Toca para ver más pasos...

Paso 2.1

Reescribe

\tan (x)

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

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

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

Paso 2.2

Reescribe

\cot (x)

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

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

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

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

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

Paso 3

Combina

\frac{1}{\sin (x)}

$\frac{1}{\sin (x)}$ y

\cos (x)

$\cos (x)$ .

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

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

Paso 5

Multiplica

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

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

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

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

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

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

Paso 6

Separa las fracciones.

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

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

Paso 7

Convierte de

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

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

\cot (x)

$\cot (x)$ .

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

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

Paso 8

Simplifica cada término.

Toca para ver más pasos...

Paso 8.1

Convierte de

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

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

\tan (x)

$\tan (x)$ .

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

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

Paso 8.2

Convierte de

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

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

\cot (x)

$\cot (x)$ .

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

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

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

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

Paso 9

Combina

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

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

\cot (x)

$\cot (x)$ .

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

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