Question

Simplifique:
a) cotgx.senx/cosx
b) senx.cosx/cotgx

Answer 1

a)
$\cot x = \dfrac{\cos x}{\sin x}\\ \\ \dfrac{\cos x}{\sin x} \cdot \dfrac{\sin x}{\cos x} = \boxed{1}$

b)
$E=\dfrac{\sin x\cdot \cos x}{\dfrac{\cos x}{\sin x}}\\ \\ \\ E=\dfrac{\sin x\cdot \cos x\cdot \sin x}{\cos x}\\ \\ \\ \boxed{E=\sin^2 x}$

Answer 2

Oie, tudo bom?

a)

$= \frac{ \cot(x) \sin(x) }{ \cos(x) } \\ = \frac{ \frac{ \cos(x) }{ \sin(x) } \: . \: \sin(x) }{ \cos(x) } \\ = \frac{ \cos(x) }{ \cos(x) } \\ \boxed{ = 1}$

b)

$= \frac{ \sin(x) \cos(x) }{ \cot(x) } \\ = \frac{ \sin(x) \cos(x) }{ \frac{ \cos(x) }{ \sin(x) } } \\ = \sin(x) \cos(x) \div \frac{ \cos(x) }{ \sin(x) } \\ = \sin(x) \cos(x) \: . \: \frac{ \sin(x) }{ \cos(x) } \\ = \frac{ \sin(x) \cos(x) \sin(x) }{ \cos(x) } \\ = \sin(x) \sin(x) \\ \boxed{ = \sin(x) {}^{2} }$

Att. NLE Top Shotta