We have to prove the identity:

`1/(tan^2x) - 1/(cot^2x) = csc^2x - sec^2x`

`1/(tan^2x) - 1/(cot^2x)`

=> `(cos^2x)/(sin^2x) - (sin^2x)/(cos^2x)`

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

=> `1/(sin^2x) - 1 - 1/(cos^2x) + 1`

=> `1/sin^2x - 1/cos^2x`

=> `csc^2x - sec^2x`

**This proves the identity: **`1/(tan^2x) - 1/(cot^2x) = csc^2x - sec^2x`

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now