Question

Find an identity for cos(4t) in terms of cos(t)
cos(4t)=

Answer 1

Use double angle formula for cosine:

`cos (2a) = 2cos^2(a) - 1`

Apply to cos(4t)

`cos (2(2t)) = 2 cos^2 (2t) - 1 \\ cos (2t) = 2 cos^2 t - 1`
Sub 2nd equation into 1st equation:

`cos(4t) = 2 (2 cos^2 t -1)^2 - 1 \\ = 8 cos^4 t -8cos^2 t +1`