Question

а)3cos(5x )=√2;
б)−2 cos( x\6 )=√3.

Answer 1

$3cos(5x)=\sqrt{2} \\cos(5x)=\frac{\sqrt{2} }{3} \\\\5x=\pm arccos(\frac{\sqrt{2} }{3})+2\pi k , k \in Z \ (:5)\\x=\frac{\pm arccos(\frac{\sqrt{2} }{3}) }{5}+\frac{2\pi k }{5}, k \in Z$

$-2cos(\frac{x}{6})=\sqrt{3} \\cos(\frac{x}{6} )=-\frac{\sqrt{3} }{2} \\\frac{x}{6}=\pm(\pi -\frac{\pi }{6})+2\pi k , k \in Z \ (*6)\\x=\pm 5\pi +12\pi k , k \in Z$