1. The problem statement, all variables and given/known data Find an albebraic expression for cos((1/3)*arccos(x)), in order to get rid of the trigonometric operands. 2. Relevant equations cos(arccos(x))=x 3. The attempt at a solution cos(x)= 4cos(x/3)^3 - 3cos(x/3), I can reduce cos(cos(x)/3) by noting that cos(arccos(x))=x. Then I solve the cubic: 1 = 4y^3 - 3y This was a tips I have found, but, it gave me nothing :P Need help!