Express cos 4 x in terms of cos x.

Question

a. cos³x - 3 sin² x cos x

b. 2 sin x cos³x - 4 sin³x cos x

c. cos⁴x - 6 sin²x cos²x + sin⁴x

d. 3 sin x - 4 sin³x

Answer 1

Using cos(x+y) formula, and cos2x formula(=cos² x - sin² x), the answer is C as the following:

cos 4x = cos (2x +2x)= cos2x cos2x- sin2x sin2x = (cos² x - sin² x)² -(2sinxcosx)²

= cos⁴ x - 2cos² x sin² x + sin⁴ x - 4sin² x cos² x

Combine like terms = cos⁴ x - 6cos² x sin² x + sin⁴ x