Question

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Answer 1

$cos(\frac{x}{4}+\frac{\pi}{3})=\frac{\sqrt2}{2}\\\\\frac{x}{4}+\frac{\pi}{3}=^+_-(\pi-\frac{\pi}{4})+2\pi k\\\\\frac{x}{4}+\frac{\pi}{3}=^+_-\frac{3\pi}{4}+2\pi k\\\\1) \\\frac{x}{4}= \frac{3\pi}{4}-\frac{\pi}{3}+2\pi k= \frac{5\pi}{12} + 2 \pi k \\x=\frac{5\pi}{3}+8 \pi k ; k \in Z\\2)\\\frac{x}{4}=-\frac{3\pi}{4}-\frac{\pi}{3}+2\pi k= -\frac{13\pi}{12}+2\pi k\\x=-\frac{13\pi}{3}+8\pi k ; k \in Z$