can you explain so i can understand?

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 = [sin² 5x]²

sin² 5x = (1 - cos 2(5x)) / 2

sin² 5x = (1 - cos 10x) / 2

[sin² 5x]² = [(1 - cos 10x) / 2]²