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Question
Prove the following trigonometric identities.
(sec2 θ − 1) (cosec2 θ − 1) = 1
Solution
We know that
`sec^2 theta - tan^2 theta = 1`
`cosec^2 theta - cot^2 theta = 1`
So,
`(sec^2 theta - 1)(cosec^2 theta - 1) = tan^2 theta xx cot^2 theta`
`= (tan theta xx cot theta)`
`= (tan theta xx 1/tan theta)^2`
`= (1)^2`
=1
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