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Question
Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.
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Solution
LHS = `sqrt(2 + tan^2 θ + cot^2 θ)`
= `sqrt( tan^2 θ + cot^2θ + 2tan θ.cot θ)` ...[ ∵ tan θ.cot θ = 1 ]
= `sqrt( tan^2 θ + cot^2θ)`
= tan θ + cot θ
= RHS
Hence proved.
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