Use half angle formulas to fill in the blanks in the identity below: (sin(3𝑥))^4 = ______ −1/2cos (____ 𝑥)+1/8cos(______ x )

Answer 1

[sin(3x)]⁴ = [√{(1 - cos(6x))/2}]⁴ = (1 - cos(6x))² / 4 = (1 - 2cos(6x) + cos²(6x)) / 4 =

1/4 - (1/2)cos(6x) + (1/4)√{(1 + cos(12x))/2)}² = 1/4 - (1/2)cos(6x) + (1/4)(1/2 + (1/2)cos(12x)) =

3/8 - (1/2)cos(6x) + (1/8)cos(12x)