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Prove the Following Trigonometric Identities. (Sec2 θ − 1) (Cosec2 θ − 1) = 1 - CBSE Class 10 - Mathematics

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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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Solution Prove the Following Trigonometric Identities. (Sec2 θ − 1) (Cosec2 θ − 1) = 1 Concept: Trigonometric Identities.
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