Sin²2x-sin²4x=sin²3x-sin²5x
1/2(1-cos4x)-1/2(1-cos8x)=1/2(1-cos6x)-1/2(1-cos10x)
1-cos4x-1+cos8x=1-cos6x-1+cos10x
(cos8x-cos4x)-(cos10x-cos6x)=0
-2sin6xsin2x+2sin8xsin2x=0
2sin2x(sin8x-sin6x)=0
2sin2x*2sinxcos7x=0
sin2x=0⇒2x=πn⇒x=πn/2
sinx=0⇒x=πn
cos7x=0⇒7x=π/2+πn⇒x=π/14+πn/7
Ответ x=πn/2 и x=π/14+πn/7