Álgebra Ejemplos

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

Paso 1

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

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

Paso 2

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

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

Paso 3

Multiplica el numerador por la recíproca del denominador.

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

Paso 4

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

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

Paso 5

Separa las fracciones.

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

Paso 6

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

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

Paso 7

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

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

Paso 8

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

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