Question

How do you simplify `cot^2x - cot^2x cos^2x`?

Answer 1

`cos^2 x`

Explanation:

Given: `cot^2x - cot^2 x cos^2x`

Factor: `cot^2x (1 - cos^2x)`

Use the Pythagorean trigonometric identity: `sin^2x + cos^2x = 1`

Rearrange the identity: `sin^2x = 1 - cos^2x`

`cot^2x (1 - cos^2x) = cot^2x sin^2x`

Use the identity: `cot x= (cos x)/(sin x)`

Realize that `cot^2x = (cot x)^2`

`cot^2x (1 - cos^2x) = (cos^2 x)/cancel(sin^2 x) cancel(sin^2x) = cos^2x`