Answer:
(1/8)(cos(4x) -4cos(2x) +3)
Step-by-step explanation:
Your answer is correct as far as it goes. You now need to use a power-reducing identity on the cos(2x)² term in your answer. The appropriate one is ...
cos(x)² = (1/2)(1 +cos(2x))
In the context of this problem, using this formula gives you ...
sin(x)⁴ = (1/4)(1 -2cos(2x) +(1/2)(1 +cos(4x))
sin(x)⁴ = (1/8)(cos(4x) -4cos(2x) +3)
