Решить уравнение:   cos^2 x + cos^2 2x+ cos^2 3x = 3/2

                                                       Решение:   2cos^2 x + 2cos^2 2x+ 2cos^2 3x = cos^2(x)+sin^2(x)+cos^2(2x)+sin^2(2x)+cos^2(3x)+sin^2(3x) cos2x+cos4x+cos6x=2cos4xcos2x+cos4x=cos4x(2cos2x+1)=0. cos4x=0 x=П/8+Пl/4 cos2x=-1/2 2x=2/3П+2Пk  x=П/3+Пk 2x=4/3П+2Пk  x=2П/3+Пk.