Prove that Cot θ. Tan (90° - θ) - Sec (90° - θ). Cosec θ + 1 = 0.

Prove that cot θ. tan (90° - θ) - sec (90° - θ). cosec θ + 1 = 0.

Sum

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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