Prove that sec^{2}θ+cosec^{2}θ can never be less than 2.
Ans: S.T Sec^{2}θ + Cosec^{2}θ can never be less than 2.
If possible let it be less than 2.
1 + Tan^{2}θ + 1 + Cot^{2}θ < 2.
⇒ 2 + Tan^{2}θ + Cot^{2}θ
⇒ (Tanθ + Cotθ)2 < 2.
Which is not possible.