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

2 Answers | Add Yours

Top Answer

justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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`

lochana2500's profile pic

lochana2500 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

L:H:S ≡ 1/tan²x - 1/cot²x

= cot²x - tan²x

⇒ use the identities cot²θ = cosec²θ - 1 & tan²θ = sec²θ -1

= cosec²x - 1 - (sec²x -1)

= cosec²x - sec²x

= R:H:S

We’ve answered 318,915 questions. We can answer yours, too.

Ask a question