Question

Como resolver a equação:
Para 0 ≤ x ≤ 2

c) 2cos² (x) - √3 . cos (x) = 0

Answer 1

$2\cdot\cos^2x-\sqrt{3}\cdot\cos\,x=0\\\\\cos\,x(2\cos\,x-\sqrt{3})=0\\\\\begin{cases}\cos\,x=0\Rightarrow\,x=\frac{\pi}{2}\;\text{e}\;\frac{3\pi}{2}\\\2\cos\,x-\sqrt{3}=0\Rightarrow\cos\,x=\frac{\sqrt{3}}{2}\Rightarrow\,x=\frac{\pi}{6}\;\text{e}\;\frac{11\pi}{6}\end{cases}$
 
 Portanto, $\boxed{S=\left\{\frac{\pi}{2},\frac{3\pi}{2},\frac{\pi}{6},\frac{11\pi}{6}\right\}}$.