Question

Prove that √(sec^2θ + cosec^2 θ) = tanθ + cotθ

Answer 1

L.H.S
√sec2θ + cosec2θ
= √(tan2θ + 1 + cot2θ + 1)
= √(tan2θ + 2 + cot2θ)
= √(tan2θ + 2tanθ cotθ + cot2θ)
{tanθ x cotθ = 1}
√(tanθ + cotθ)2
= tanθ ≠  cotθ