Question

корень из 3 sin2x-cos2x =2

Answer 1

$sqrt3sin2x-cos2x=2|:2\frac{sqrt3}{2}sin2x-frac{1}{2}cos2x=1\frac{sqrt3}{2}=cosfrac{pi}{6}, ; ; frac{1}{2}=sinfrac{pi}{6};\sin2xcosfrac{pi}{6}-cos2xsinfrac{pi}{6}=1\sin(2x-frac{pi}{6})=1\2x-frac{pi}{6}=frac{pi}{2}+2pi n\2x=frac{2pi}{3}+2pi n\x=frac{pi}{3}+pi n, ; nin Z.$