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Question
Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.
Solution
LHS = cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1
= cot θ. cot θ - cosec θ. cosec θ + 1
= (cot2θ - cosec2θ) + 1
= - 1 + 1 = 0
= RHS
Hence proved.
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