1) given the double angle identity for cosine: cos2θ=cos2θ-sin2θ
Prove: cos3θ = cos3θ - 3cosθsin2θ
and: cos4θ = cos4θ - 6cos2θsin2θ + sin2θ
2) Continue this process, finding an identity for cos5θ and cos6θ.
3) By examining the above identities (and a few more if needed), try to identify a pattern in order to generalize an identity for cosnθ.
(HINT: You will need to look at Pascal's Triangle.)