Factor the expression. use the fundamental identities to simplify, if necessary.

see explanation

Step-by-step explanation:

Using the trigonometric identity

sin²x + cos²x = 1 ⇒ sin²x = 1 - cos²x

Given

sin²x + 7cosx + 17

=1 - cos²x + 7cosx + 17

= - cos²x + 7cosx + 18 ← factor out - 1 from each term

= - (cos²x - 7cosx - 18)

Consider the factors of the constant term (- 18) which sum to give the coefficient of the cosx term (- 7)

The factors are - 9 and + 2, thus

= - (cosx - 9)(cosx + 2) ← in factored form