Question

Prove the following trigonometric identities.

`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`

Answer 1

L.H.S = `cot^2 A cosec^2B - cot^2 B cosec^2 A`

`= cot^2 A(1+ cot^2 B) - cot^2   B(1 + cot^2 A)`    (∵ `1 + cot^2 theta = cosec^2 theta`)

`= cot^2 A + cot^2 A cot^2 B - cot^2 B cot^2 A`

`= cot^2 A - cot^2 B`

Hence proved