Question:
If sin θ + cosec θ = 2, then sin2θ + cosec2θ is equal to
(a) 1
(b) 4
(c) 2
(d) none of these
Solution:
Given sinθ + cosecθ = 2
⇒ (sinθ + cosecθ)2 = 4
i.e sin2θ + cosec2θ + 2 sinθ cosecθ = 4
i. e $\sin ^{2} \theta+\operatorname{cosec}^{2} \theta+2 \sin \theta \frac{1}{\sin \theta}=4$
i. e $\sin ^{2} \theta+\operatorname{cosec}^{2} \theta=2$
Hence, the correct answer is option C.
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