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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.
Prove that a simple graph is connected if and only if it has a spanning tree. Ans: First assume that a simple graph G has a spanning tree T. T consists of every node of G.
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