Question

How do you use the power reducing formulas to rewrite the expression `cos^4x` in terms of the first power of cosine?

Answer 1

`cos^4 x = 1/8 (3 + 4 cos 2x + cos 4x)`

Explanation:

`cos 2x = 2 cos^2 x - 1`

`cos ^2 x =1/2 ( 1 + cos 2x)`

`cos^2 2x = 1/2 ( 1 + cos 4x)`

`cos^4 x = (cos ^ 2 x)^2 = 1/4 (1 + 2 cos 2x + cos ^2 2x)`

`cos^4 x = 1/4 (1 + 2 cos 2x + 1/2( 1 + cos 4x) )`

`cos^4 x = 1/8 (3 + 4 cos 2x + cos 4x)`