Question

Resolva a equação cosseno ,(X + π\5) = √2/2

Answer 1

$\mathsf{\cos(x+\dfrac{\pi}{5}) =\dfrac{\sqrt{2}}{2}}$

$\mathsf{\cos(x+\dfrac{\pi}{5}) =\cos(\dfrac{\pi}{4})}$

$\mathsf{x+\dfrac{\pi}{5}=\dfrac{\pi}{4}}\\\mathsf{x=\dfrac{\pi}{4}-\dfrac{\pi}{5}}$

$\mathsf{x=\dfrac{5\pi-4\pi}{20}=\dfrac{\pi}{20}+2k\pi\,k\in\,\mathbb{Z}}$

$\mathsf{x+\dfrac{\pi}{5}=\dfrac{7\pi}{4}} \\\mathsf{x=\dfrac{7\pi}{4}-\dfrac{\pi}{5}} \\\mathsf{x=\dfrac{35\pi-4\pi} {5}} \\\mathsf{x=\dfrac{31\pi}{5}+2k\pi\,k\in\,\mathbb{Z}}$