Trigonometria Exemplos

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

Etapa 1

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

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

Etapa 2

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

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

Etapa 3

Multiplique o numerador pelo inverso do denominador.

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

Etapa 4

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

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

Etapa 5

Separe as frações.

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

Etapa 6

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

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

Etapa 7

Converta de $\frac{1}{\sin (x)}$ em $\csc (x)$ .

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

Etapa 8

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

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