Álgebra Exemplos

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

Etapa 1

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

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

Etapa 2

Simplifique o denominador.

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Etapa 2.1

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

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

Etapa 2.2

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

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

Etapa 3

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

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

Etapa 4

Multiplique o numerador pelo inverso do denominador.

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

Etapa 5

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

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

Etapa 6

Separe as frações.

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

Etapa 7

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

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

Etapa 8

Simplifique cada termo.

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Etapa 8.1

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

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

Etapa 8.2

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

$\frac{1}{\tan (x) + \cot (x)} \cot (x)$

Etapa 9

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

$\frac{\cot (x)}{\tan (x) + \cot (x)}$