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

Question

Hello, I need help on how to power reduce cos⁴(2x). I've watched multiple videos but still don't understand.

Answer 1

cos⁴ (2x)

[cos² (2x)][cos² (2x)]

[(1 + cos 4x) / 2][(1 + cos 4x) / 2]

(1 + 2 cos 4x + cos² 4x) / 4

[(1 + 2 cos 4x) / 4] + [(cos² 4x) / 4]

cos² 4x = (1 + cos 8x) / 2

[(1 + 2 cos 4x) / 4] + [((1 + cos 8x) / 2) / 4]

[(1 + 2 cos 4x) / 4] + [(1 + cos 8x) / 8]

[2(1 + 2 cos 4x) / 8] + [(1 + cos 8x) / 8]

[2 + 4 cos 4x) / 8] + [(1 + cos 8x) / 8]

[3 + 4 cos 4x + cos 8x] / 8