Cos(4x)+8sin^2 (x)-2=6cos(2x)-8cos^4 (x)

cos(4x) + 8sin^2 x - 2 = 6cos(2x) - 8cos^4 x2cos^2(2x) - 1 + 8(1 - cos^2 x) - 2 = 6(2cos^2 x - 1) - 8cos^4 x2(2cos^2 x - 1)^2 - 1 + 8 - 8cos^2 x - 2 = 12cos^2 x - 6 - 8cos^4 x2(4cos^4 x - 4cos^2 x + 1) + 11 - 8cos^2 x = 12cos^2 x - 8cos^4 x8cos^4 x - 8cos^2 x + 2 + 11 - 8cos^2 x = 12cos^2 x - 8cos^4 x16cos^4 x - 28cos^2 x + 11 = 0Квадратное уравнение относительно cos^2 xD/4 = 14^2 - 16*11 = 196 - 176 = 20cos^2 x = (14 - √20)/16 = (14 - 2√5)/16 = (7 - √5)/8 ~ 0,5955cos^2 x = (14 + √20)/16 = (14 + 2√5)/16 = (7 + √5)/8 ~ 1,15 > 1 - решений нетcos x1 = - √((7 - √5)/8)cos x2 = √((7 - √5)/8)