Factor the algebraic expression below in terms of a single trigonometric function csc² x - 1

Solution:

Given, cosec²x - 1

We have to find the single trigonometric function.

We know, cosec x = 1/sin x

Now, (1/sin²x) - 1

By cross multiplication,

(1 - sin²x)/sin²x

We know, sin²x + cos²x = 1

So, 1 - sin²x = cos²x

Now, (cos²x)/sin²x

= cot²x

Therefore, the algebraic expression is cot²x.

Factor the algebraic expression below in terms of a single trigonometric function csc² x - 1

Solution:

The algebraic expression in terms of a single trigonometric function csc²x - 1 is cot²x.