Trigonometria Exemplos

$\frac{\csc (x) \cos^{2} (x)}{1 + \csc (x)}$

Etapa 1

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

$\frac{\frac{1}{\sin (x)} \cos^{2} (x)}{1 + \csc (x)}$

Etapa 2

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

$\frac{\frac{1}{\sin (x)} \cos^{2} (x)}{1 + \frac{1}{\sin (x)}}$

Etapa 3

Combine $\frac{1}{\sin (x)}$ e $\cos^{2} (x)$ .

$\frac{\frac{\cos^{2} (x)}{\sin (x)}}{1 + \frac{1}{\sin (x)}}$

Etapa 4

Multiplique o numerador pelo inverso do denominador.

$\frac{\cos^{2} (x)}{\sin (x)} \cdot \frac{1}{1 + \frac{1}{\sin (x)}}$

Etapa 5

Multiplique $\frac{\cos^{2} (x)}{\sin (x)}$ por $\frac{1}{1 + \frac{1}{\sin (x)}}$ .

$\frac{\cos^{2} (x)}{\sin (x) (1 + \frac{1}{\sin (x)})}$

Etapa 6

Fatore $\cos (x)$ de $\cos^{2} (x)$ .

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

Etapa 7

Separe as frações.

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

Etapa 8

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

$\frac{\cos (x)}{1 + \frac{1}{\sin (x)}} \cot (x)$

Etapa 9

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

$\frac{\cos (x)}{1 + \csc (x)} \cot (x)$

Etapa 10

Combine $\frac{\cos (x)}{1 + \csc (x)}$ e $\cot (x)$ .

$\frac{\cos (x) \cot (x)}{1 + \csc (x)}$