If sin θ + cosec θ = 2,
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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