Trigonometria Exemplos

$5 \sin^{2} (x) \csc^{2} (x) - 5 \sin^{2} (x)$

Etapa 1

Reordene $5 \sin^{2} (x) \csc^{2} (x)$ e $- 5 \sin^{2} (x)$ .

$- 5 \sin^{2} (x) + 5 \sin^{2} (x) \csc^{2} (x)$

Etapa 2

Fatore $5 \sin^{2} (x)$ de $- 5 \sin^{2} (x)$ .

$5 \sin^{2} (x) (- 1) + 5 \sin^{2} (x) \csc^{2} (x)$

Etapa 3

Fatore $5 \sin^{2} (x)$ de $5 \sin^{2} (x) \csc^{2} (x)$ .

$5 \sin^{2} (x) (- 1) + 5 \sin^{2} (x) (\csc^{2} (x))$

Etapa 4

Fatore $5 \sin^{2} (x)$ de $5 \sin^{2} (x) (- 1) + 5 \sin^{2} (x) (\csc^{2} (x))$ .

$5 \sin^{2} (x) (- 1 + \csc^{2} (x))$

Etapa 5

Reorganize os termos.

$5 \sin^{2} (x) (\csc^{2} (x) - 1)$

Etapa 6

Aplique a identidade trigonométrica fundamental.

$5 \sin^{2} (x) \cot^{2} (x)$

Etapa 7

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

$5 \sin^{2} (x) {(\frac{\cos (x)}{\sin (x)})}^{2}$

Etapa 8

Aplique a regra do produto a $\frac{\cos (x)}{\sin (x)}$ .

$5 \sin^{2} (x) \frac{\cos^{2} (x)}{\sin^{2} (x)}$

Etapa 9

Cancele o fator comum de $\sin^{2} (x)$ .

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Etapa 9.1

Fatore $\sin^{2} (x)$ de $5 \sin^{2} (x)$ .

$\sin^{2} (x) \cdot 5 \frac{\cos^{2} (x)}{\sin^{2} (x)}$

Etapa 9.2

Cancele o fator comum.

$\sin^{2} (x) \cdot 5 \frac{\cos^{2} (x)}{\sin^{2} (x)}$

Etapa 9.3

Reescreva a expressão.

$5 \cos^{2} (x)$