Trigonometría Ejemplos

$\frac{\cot (x)}{\csc (x) - \sin (x)}$

Paso 1

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

$\frac{\frac{\cos (x)}{\sin (x)}}{\csc (x) - \sin (x)}$

Paso 2

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

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

Paso 3

Multiplica el numerador por la recíproca del denominador.

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

Paso 4

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

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

Paso 5

Separa las fracciones.

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

Paso 6

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

$\frac{1}{\frac{1}{\sin (x)} - \sin (x)} \cot (x)$

Paso 7

Convierte de $\frac{1}{\sin (x)}$ a $\csc (x)$ .

$\frac{1}{\csc (x) - \sin (x)} \cot (x)$

Paso 8

Combina $\frac{1}{\csc (x) - \sin (x)}$ y $\cot (x)$ .

$\frac{\cot (x)}{\csc (x) - \sin (x)}$