Question

Expand --> cos(4x)cos(x) =?

Answer 1

Use double formula of cosines
\[\cos (2x) = 2\cos ^{2}(x)\]We first calculate cos(4x) in terms of cos(x)\[\cos(4x) = 2\cos ^{2}(2x) - 1\]\[2[2\cos ^{2}(x) - 1]^{2} -1\]\[8\cos ^{2}(x) - 8\cos(x) + 1\]Then multiply the last line by cos(x) to get\[8\cos ^{3}(x) - 8\cos ^{2}(x) + \cos(x)\]