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Question
Prove the following trigonometric identities.
`cot^2 A cosec^2B - cot^2 B cosec^2 A = cot^2 A - cot^2 B`
Solution
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
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