Question

решите уравнение
1/2cos2x+($sqrt{3}$)/2sin2x=1

Answer 1

$frac{1}{2}cos2x+frac{sqrt3}{2} sin2x=1\\sinfrac{pi}{6}cdot cos2x+cosfrac{pi}{6}cdot sin2x=1\\sin(2x+frac{pi}{6})=1\\2x+frac{pi}{6}=frac{pi}{2}+2pi n,; nin Z\\2x=-frac{pi}{6}+frac{pi}{2}+2pi n,; nin Z\\2x=frac{pi}{3}+2pi n,; nin Z\\x=frac{pi}{6}+pi n ,; nin Z$