Решить уравнениеsin^2x+sin^2(2x)-sin^2(3x)-sin^2(4x)=0

sin²x+sin²2x-sin²3x-sin²4x=0 1/2(1-cos2x)+1/2(1-cos4x)-1/2(1-cos6x)-1/2(1-cos8x)=0 1-cos2x+1-cos4x-1+cos6x-1+cos8x=0 (cos8x-cos2x)+9cos6x-cos4x)=0 -2sin3xsin5x-2sin2xsin5x=0 -2sin5x(sin3x+sin2x)=0 -4sin5xsin2,5xcos0,5x=0 sin5x=0⇒5x=π4⇒x=πn/5 sin2,5x=0⇒2,5x=πn⇒x=2π/5 cos0.5x=0⇒0,5x=π/2+πn⇒x=π+2πn Ответ x=πn/5 ,x=π+2πn