Question

Factor the algebraic expression below in terms of a single trigonometric function cos x - sin 2x - 1

Answer 1

(cosx+2)(cosx-1)

Explanation:

cos x - sin²x - 1

sin²x = 1- cos²x

plug in

cos x - (1- cos²x) - 1 = cos x - 1 + cos²x - 1 = cos²x + cos x - 2

factor cos²x + cos x - 2

(cosx+2)(cosx-1)

Answer 2

cos x - sin² x - 1 =
= cos x - ( cos² x - 1 ) - 1 =
= cos x - cos² x + 1 - 1 =
= cos x - cos² x =
= cos x · ( 1 - cos x )