Question

resolva as equações para 0<x<2pi
2*cos^2 x - raiz(3) * cos x =0

Answer 1

Temos que

$2 \cos^2(x)- \sqrt{3} \cos(x) = 0 \Rightarrow \cos(x) . (2\cos(x)-\sqrt{3})=0$

Portanto temos que

$\cos(x) = 0 \Rightarrow x = \frac{\pi}{2} \, \, (90^{o})\, \, ou \, \, x = \frac{3\pi}{2} \, \, (270^{o})$

ou 

$2\cos(x) - \sqrt{3} = 0 \Rightarrow 2\cos(x) = \sqrt{3} \Rightarrow \cos(x) = \displaystyle\frac{\sqrt{3}}{2}$

$x = \frac{\pi}{6} \, \, (30^{o}) \, \, ou \, \, x = \frac{11\pi}{6} \, \, (330^{o})$