Question

simplifique a expressão : $\frac{1 - sen^{2}x }{cotgx.senx}$

Answer 1

Temos que:

$sen^2(x) +cos^2(x) = 1 ~~\to~~ cos^2(x) = 1 - sen^2(x)$

$cotg(x) = \dfrac{1}{tg(x)} = \dfrac{cos(x)}{sen(x)}$

Logo:

$= \dfrac{1 - sen^2(x)}{cotg(x)*sen(x)} \\ \\ \\ = \dfrac{cos^2(x)}{ \dfrac{cos(x)}{sen(x)} * sen(x) } \\ \\ \\ = \dfrac{cos^2(x)}{cos(x)} \\ \\ \\ = cos(x)$