Pré-cálculo Exemplos

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

Etapa 1

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

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

Etapa 2

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

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

Etapa 3

Multiplique o numerador pelo inverso do denominador.

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

Etapa 4

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

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

Etapa 5

Separe as frações.

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

Etapa 6

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

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

Etapa 7

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

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

Etapa 8

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

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