Use the power-reducing formulas as many times as possible to rewrite the expression in terms of the first power of the cosine.

7 cos4 x

Ruublrr Dec 1, 2018

#1**+1 **

\(\text{I assume you mean }7\cos^4(x)\)

\(\cos^4(x) =\left( \cos^2(x)\right)^2 = \\ \left(\dfrac{\cos(2x)+1}{2}\right)^2 = \\ \dfrac 1 4 + \dfrac 1 2 \cos(2x) + \dfrac 1 4 \cos^2(2x)\\ \text{repeat the process on the term on the right}\\ \dfrac 1 4 \cos^2(2x) = \dfrac 1 8 (1 + \cos(4x)) \\ \text{so combining everything}\\ 7\cos^4(x) = \dfrac{7}{8} (4 \cos (2 x)+\cos (4 x)+3)\)

.Rom Dec 1, 2018