Expressing cos^6(x)?

[patton_223]

1. The problem statement, all variables and given/known data
Express cos^6(x) in a form that does not involve powers of trig functions


2. Relevant equations

idk actually........binomial theorem? algebra? lol


3. The attempt at a solution

ok, so i realized that it can be expressed as (cos^2(x))^3

and that can be ((cos(2x) + 1)/2)^3

and that can be expanded as

1/8+3/8 cos(2 x)+3/8 cos^2(2 x)+1/8 cos^3(2 x)

but how do i get the answer with no powers in in? idk what to do up until that point

[SammyS]

You already showed how to handle cos2(x). Do a similar thing with cos2(2x).