Решите уравнение cos^2 x+sqrt(3)sin^2 x=(1+sqrt(3))(cos x-cos xsin x+sin x).

cos^2 x+sqrt(3)sin^2 x=(1+sqrt(3))(cos x-cos xsin x+sin x) ^2 x+(1+sqrt(3))cos xsin x+sqrt(3)sin^2 x=(1+sqrt(3))(cos x+sin x) (cos x+sin x)(cos x+sqrt(3)sin x)=(1+sqrt(3))(cos x+sin x) (cos x+sin x)((1)/(2)cos x+(sqrt(3))/(2)sin x-(1+sqrt(3))/(2))=0 (x-(pi)/(4))(cos(x-(pi)/(3))-(1+sqrt(3))/(2))=0 (x-(pi)/(4))=0 x-(pi)/(4)=(pi)/(2)+kpi, kinZ x=(3pi)/(4)+kpi, kinZ.

\(x=\frac{3\pi}{4}+k\pi,\ k\in\mathbb{Z}\)