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Question

If sin θ + cosec θ = 2, then sin2θ + cosec2θ is equal to
(a) 1
(b) 4
(c) 2
(d) none of these

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Solution

Given sinθ + cosecθ = 2
⇒ (sinθ + cosecθ)2 = 4
i.e sin2θ + cosec2θ + 2 sinθ cosecθ = 4
i.e sin2θ+cosec2θ+2sinθ1sinθ=4i.e sin2θ+cosec2θ=2

Hence, the correct answer is option C.

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