Question

а)3cos(5x )=√2;
б)−2 cos( x6 )=√3.

Answer 1

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

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