Question

Precalc.

Problem attached.

A full explanation will be rewarded.

Answer 1

`\bf cos(2x)=-\cfrac{√(2)}{2}\implies cos^(-1)[cos(2x)]=cos^(-1)\left( -\cfrac{√(2)}{2} \right) \\\\\\ \measuredangle 2x=cos^(-1)\left( -\cfrac{√(2)}{2} \right)\implies \measuredangle 2x= \begin{cases} (3\pi )/(4)\\\\ (5\pi )/(4) \end{cases}\\\\ -------------------------------\\\\ x=\cfrac{3\pi }{2\cdot 4}\implies \measuredangle x=\cfrac{3\pi }{8}\\\\ -------------------------------\\\\ x=\cfrac{5\pi }{2\cdot 4}\implies \measuredangle x=\cfrac{5\pi }{8}`