Use half angle or power reduction formulas to fill in the blanks in the identity below:

Question

Use half angle or power reduction formulas to fill in the blanks in the identity below:

(sin(5x))^4 =___ -1/2cos(___ x ) +( +1/8cos(___ x )

Answer 1

sin⁴(5x) = (1 - cos(10x))²/4 = 1/4 - 1/2cos10x + 1/4cos²(10x) = 1/4 - 1/2cos(10x) +1/8(1 + cos(20x)) =

3/8 - 1/2cos(10x) + 1/8cos(20x)