Решите уравнение: sin^2 2x+sin^2 3x=sin^2 4x+sin^2 5x

1/2 (1-cos4x) + 1/2 (1-cos6x) = 1/2 (1-cos8x) + 1/2 (1-cos10x)

1-cos4x+1-cos6x=1-cos8x+1-cos10x

cos10x-cos6x + cos8x-cos4x=0

-2sin8xsin2x-2sin6xsin2x=0

-2sin2x (sin8x+sin6x) = 0

-2sin2x*2sin7xcosx=0

sin2x=0⇒2x=πn⇒x=πn/2

sin7x=0⇒7x=πn⇒x=πn/7

cosx=0⇒x=π/2+πn