sinx cos6x - sin3x cos4x =

= 1/2 * (sin7x + sin(-5x)) - 1/2 * (sin7x + sin(-x)) =

= 1/2 * (sin7x - sin5x) - 1/2 * (sin7x - sinx) =

= 1/2 * (sin7x - sin5x - sin7x + sinx) =

= 1/2 * (sinx - sin5x) =

= 1/2 * 2 * sin(-2x) * cos3x =

= sin(-2x) * cos3x = - sin2x * cos3x