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Question:

Show that √(1+sinθ)/(1-sinθ) = (1+sinθ)/cosθ

Solution:

LHS: √(1+sinθ)/(1-sinθ) = √((1+sinθ)/(1-sinθ) × (1+sinθ)/(1+sinθ)) = √((1+sinθ)²/(1-sin²θ)) = √((1+sinθ)²/cos²θ) = (1+sinθ)/cosθ