Question

Resolver em R a equação 2cos(2x) -1=0

Answer 1

Olá, Bruno.

$2\cos(2x)-1=0\Rightarrow \cos(2x)=\frac12\Rightarrow\cos^2x-\sin^2x=\frac12\Rightarrow\\\\ 1-\sin^2x-\sin^2x=\frac12\Rightarrow-2\sin^2x=\frac12-1\Rightarrow 2\sin^2x=\frac12\Rightarrow\\\\ \sin^2x=\frac14\Rightarrow\sin x=\pm\sqrt\frac14=\pm\frac12\Rightarrow\\\\ \boxed{x=\pm\frac\pi 6+2k\pi,k\in\mathbb{Z}}\text{ ou }\boxed{x=\pm\frac{5\pi} 6+2k\pi,k\in\mathbb{Z}}$