Question

Factor the algebraic expression below in terms of a single trigonometric function.

Answer 1

Let a = sin x.

Hence, the expression will become:

`a^2+a-2`

Then, let's factor out the expression above. Here are the steps:

1. Find factors of the constant term -2 that will result in the middle term which is 1.

Factors of -2 are:

a. 1 and -2 → sum is -1

b. -1 and 2 → sum is 1

Hence, the factors of -2 that will result in 1 are -1 and 2.

2. Applying the factors -1 and 2, the factors of the expression are:

`(a-1)(a+2)`

Since we let a = sin x, replace "a" in the factors above with sin x.

The factors of the given algebraic expression are [sin (x) - 1][sin (x) + 2].

`[sin(x)-1][sin(x)+2]`