Question

cos(3x-π/6)+cos(x+π/4)=0

Answer 1

$cosa+cosb=2cosfrac{a+b}{2}cosfrac{a-b}{2}\\cos(3x-frac{pi}{6})+cos(x+frac{pi}{4})=0\2cos(2x-frac{pi}{6})cos(x-frac{5pi}{6})=0\\1)cos(2x-frac{pi}{6})=0\2x-frac{pi}{6}=frac{pi}{2}+pi n\2x=frac{2pi}{3}+pi n\x=frac{pi}{3}+frac{pi n}{2}, ; nin Z;\\2)cos(x-frac{5pi}{6})=0\x-frac{5pi}{6}=frac{pi}{2}+pi k\x=frac{4pi }{3}+pi k, ; kin Z.$