Question

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

Answer 1

a) cotgx*senx/cosx = 1/tgx*senx/cosx = 1/senx/cosx*senx/cosx = cosx/senx*senx/cosx=cosx/cosx = 1

b) senx*cosx/cotgx=senx*cosx/1/tgx = senx*cosx/ 1/senx/cosx = senx*cosx/cosx/senx = senx*cosx*senx/cosx = sen²x

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