Power Reducing Formula

Question

Use the power-reducing formulas to rewrite the expression in terms of first powers of the cosines of multiple angles.

sin⁴(x) cos²(x)

Answer 1

sin⁴(x)cos²(x) = 1/4(4sin²(x)cos²(x))sin²(x)) = 1/4sin²(2x)sin²(x) = 1/16(cos(x) - cos(3x))² =

1/16cos²(x) - 1/8cos(x)cos(3x) + 1/16cos²(3x) =

1/32 + 1/32cos(2x) - 1/16 cos(4x) - 1/16 cos(2x) + 1/32 + 1/32cos(6x) =

1/16 - 1/32cos(2x) - 1/16 cos(4x) + 1/32 cos(6x)

Answer was verified by comparing the final function with the initial function on [0, 2π)