Question

cos^3beta=cos^3beta-3sin^2betacosbeta

Answer 1

Are you sure BOTH are cos^3(beta) ?

Answer 2

Oh whoops! the first part is cos3(beta)! sorry about that

Answer 3

I will use "x" instead of beta as it is easier to type.
Try expanding cos(3x) by writing it as cos(x + 2x) and using the angle sum formula for cosine. Then further expand cos(2x) and simplify.

Answer 4

cos 3x = cos (x + 2x) = cos x*cos 2x - sin x*sin 2x =
= cos x*cos 2x - 2sin^2 x*cos x = (replace sin 2x by 2sin x8cos x)
= cos x(cos 2x - 2sin^2 x) = (replace cos 2x by cos^2 x - sin^2 x)
= cos x(cos^2 x - 3sin^2 x) =
Finally: cos 3x = cos^3 x - 3sin^2 x*cos x