Trigonometria Exemplos

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

Etapa 1

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

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

Etapa 2

Multiply the numerator and denominator of the fraction by $\cos (x)$ .

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Etapa 2.1

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

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

Etapa 2.2

Combine.

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

Etapa 3

Aplique a propriedade distributiva.

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

Etapa 4

Simplifique os termos.

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Etapa 4.1

Cancele o fator comum de $\cos (x)$ .

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Etapa 4.1.1

Cancele o fator comum.

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

Etapa 4.1.2

Reescreva a expressão.

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

Etapa 4.2

Multiplique $\cos (x)$ por $1$ .

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

Etapa 4.3

Fatore $\cos (x)$ de $\cos (x) \sin (x) + \cos (x) \cos (x)$ .

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Etapa 4.3.1

Fatore $\cos (x)$ de $\cos (x) \sin (x)$ .

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

Etapa 4.3.2

Fatore $\cos (x)$ de $\cos (x) \cos (x)$ .

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

Etapa 4.3.3

Fatore $\cos (x)$ de $\cos (x) (\sin (x)) + \cos (x) (\cos (x))$ .

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