trig--power reducing formulas
posted by Brian .
Having trouble with this problem:
Rewrite the expression as an equivalent expression that does not contain powers greater than 1.
My answer: cos³x=(cos²x)(cosx)
=(1+cos2x/2)(cosx)-->cos+cos³x/2...which is wrong
You have to use doubling formulas again to express it in terms of cos(3x). If you know about complex numbers then the derivation is easy:
cos(x) = [exp(i x) + exp(-i x)]/2
cos^3(x) = 1/8 [exp(3 i x) +
exp(-3 i x)+ 3 exp(ix) + 3 exp(-ix) ] =
1/4 cos(3 x) + 3/4 cos(x)