Trigonometría Ejemplos

$\frac{\tan (x)}{\sec (x) - \cos (x)}$

Step 1

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

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

Step 2

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

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

Step 3

Multiplica el numerador por la recíproca del denominador.

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

Step 4

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

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

Step 5

Separa las fracciones.

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

Step 6

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

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

Step 7

Convierte de $\frac{1}{\cos (x)}$ a $\sec (x)$ .

$\frac{1}{\sec (x) - \cos (x)} \tan (x)$

Step 8

Combina $\frac{1}{\sec (x) - \cos (x)}$ y $\tan (x)$ .

$\frac{\tan (x)}{\sec (x) - \cos (x)}$