Prove that Sqrt(2 + Tan^2 θ + Cot^2 θ) = Tan θ + Cot θ

Prove that `sqrt(2 + tan^2 θ + cot^2 θ) = tan θ + cot θ`.

Sum

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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