Решите уравнение cos 2x=(1+sqrt(3))/(2)(cos x+sin x).

cos 2x=(1+sqrt(3))/(2)(cos x+sin x) cos^2x-sin^2x=(1+sqrt(3))/(2)(cos x+sin x) [arraylcos x+sin x=0 cos x-sin x=(1)/(2)+(sqrt(3))/(2)array. [arraylcos(x-pi/4)=0 cos(x+pi/4)=cos(pi/3-pi/4)array. [arraylx=3pi/4+kpi, kinZ x=-pi/4+-pi/12+2kpi, kinZarray. [arraylx=-pi/4+kpi, kinZ x=-pi/6+2kpi, kinZ x=-pi/3+2kpi, kinZarray.

x = -\frac{\pi}{4}+k\pi,\ -\frac{\pi}{6}+2k\pi,\ -\frac{\pi}{3}+2k\pi,\ k\in\mathbb{Z}