Prove that sec2+cosec2 can never be less than 2, Mathematics

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Prove that sec²θ+cosec²θ can never be less than 2.

Ans: S.T Sec²θ + Cosec²θ can never be less than 2.

If possible let it be less than 2.

1 + Tan²θ + 1 + Cot²θ < 2.

⇒ 2 + Tan²θ + Cot²θ

⇒ (Tanθ + Cotθ)2 < 2.

Which is not possible.

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