cos7x+sin8x=cos3x-sin2x

cos7x-cos3x = - (sin8x+sin2x)

-2sin5x sin2x = - 2sin5x cos3x

2sin5x (cos3x-sin2x) = 0

1) sin5x=0, 5x=πn, x=πn/5, n∈Z

2) cos3x-sin2x=0, cos3x-cos (π/2-2x) = 0, - 2sin (π/2-x) sin (5x-π/2) = 0

sin (π/2-x) = 0, cosx=0, x=π/2+2πk, k∈Z

sin (5x-π/2) = 0, - sin (π/2-5x) = 0, cos5x=0, 5x=π/2+2πm, x=π/10+2πm/5, m∈Z