Решите уравнение cos^4 x-cos(x+(pi)/(3))cos(x-(pi)/(3))=2sin(x+(pi)/(6))sin(x-(pi)/(6)).

cos^4 x-cos(x+(pi)/(3))cos(x-(pi)/(3))=2sin(x+(pi)/(6))sin(x-(pi)/(6)) ^4 x-cos(x+(pi)/(3))cos(x-(pi)/(3))=2cos((pi)/(3)-x)cos((2pi)/(3)-x) ^4 x-cos(x+(pi)/(3))cos(x-(pi)/(3))=-2cos(x-(pi)/(3))cos(x+(pi)/(3)) ^4 x+cos(x+(pi)/(3))cos(x-(pi)/(3))=0^4 x+(1)/(2)(cos 2x+cos(2pi)/(3))=0 ^4 x+cos^2 x-(3)/(4)=0(cos^2 x-(1)/(2))(cos^2 x+(3)/(2))=0 x=+-(1)/(sqrt(2)) x=(pi)/(4)+(kpi)/(2), kinZ.

\(x=\frac{\pi}{4}+\frac{k\pi}{2},\ k\in\mathbb{Z}\)