# Factor the algebraic expression below in terms of a single trigonometric function csc^{2} x - 1

**Solution:**

Given, cosec^{2}x - 1

We have to find the single trigonometric function.

Now, (1/sin^{2}x) - 1

(1 - sin^{2}x)/sin^{2}x

We know, sin^{2}x + cos^{2}x = 1

So, 1 - sin^{2}x = cos^{2}x

Now, (cos^{2}x)/sin^{2}x

= cot^{2}x

Therefore, the algebraic expression is cot^{2}x.

## Factor the algebraic expression below in terms of a single trigonometric function csc^{2} x - 1

**Solution:**

The algebraic expression in terms of a single trigonometric function csc^{2}x - 1 is cot^{2}x.

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