Question

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

please help me, ive been struggling so hard. make it easy to follow along? i found it answered on here but it confused me. idk

Answer 1

(cosx + 2)(cosx - 1)

Explanation:

Using the trigonometric identity

cos²x + sin²x = 1 ⇒ sin²x = 1 - cos²x

Given

cosx - sin²x - 1

= cosx - (1 - cos²x) - 1

= cosx - 1 + cos²x - 1

= cos²x + cosx - 2

= (cosx + 2)(cosx - 1) ← in factored form