Trigonometria Exemplos

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

Etapa 1

Reescreva $\tan (x)$ em termos de senos e cossenos.

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

Etapa 2

Reescreva $\sec (x)$ em termos de senos e cossenos.

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

Etapa 3

Multiplique o numerador pelo inverso do denominador.

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

Etapa 4

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

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

Etapa 5

Separe as frações.

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

Etapa 6

Converta de $\frac{\sin (x)}{\cos (x)}$ em $\tan (x)$ .

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

Etapa 7

Converta de $\frac{1}{\cos (x)}$ em $\sec (x)$ .

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

Etapa 8

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

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