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Question
Prove the following identities.
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
Solution
`(1 - tan^2theta)/(cot^2 theta - 1)` = tan2 θ
L.H.S. = `(1 - tan^2theta)/(cot^2 theta - 1)`
= `1 - tan^2theta ÷ 1/(tan^2theta) - 1`
= `1 - tan^2theta ÷ (1 - tan^2theta)/(tan^2theta)`
= `(1 - tan^2theta) xx (tan^2theta)/((1 - tan^2 theta))`
= tan2 θ
L.H.S. = R.H.S.
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