Prove that Cosec2 (90° - θ) + Cot2 (90° - θ) = 1 + 2 Tan2 θ.

Prove that cosec² (90° - θ) + cot² (90° - θ) = 1 + 2 tan² θ.

Sum

LHS = cosec² (90° - θ) + cot² (90° - θ)

= sec² θ + tan²θ

= 1 + tan²θ + tan²θ

= 1 + 2 tan²θ

= RHS
Hence proved.

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