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Sum

Prove that sec^{2} (90° - θ) + tan^{2} (90° - θ) = 1 + 2 cot^{2} θ.

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#### Solution

LHS = sec^{2} (90° - θ) + tan^{2} (90° - θ)

= cosec^{2}θ + cot^{2}θ

= 1 + cot^{2}θ + cot^{2}θ

= 1 + 2cot^{2}θ

= RHS

Hence proved.

Concept: Trigonometric Identities

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