Question

Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

Answer 1

We are asked to express cos^ 3 x in terms of  powers of trigonometric functions not greater than 1

cos ^ 3 x is equal to cos x * cos^2 x. 
cos^2 x = 1 - sin^2 x.
sin^2 x  = (1 - cos 2x) /2 

the answer is cos ^ 3 x = cos x * (1 -  (1 - cos 2x) /2 )