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Question
Prove the following identities:
`(1 - tan^2 θ)/(cot^2 θ - 1) = tan^2 θ`.
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Solution
LHS = `(1 - tan^2 θ)/(cot^2 θ - 1)`
= `(1 - tan^2 θ)/(1/tan^2 θ - 1)`
= `((1 - tan^2 θ)/(1 - tan^2 θ)/tan^2 θ) `
= tan2 θ
= RHS
Hence proved.
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