If $\sin \theta+\operatorname{cosec} \theta=2$, then $\sin ^2 \theta+\operatorname{cosec}^2 \theta$ is equal to
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If $\sin \theta+\operatorname{cosec} \theta=2$, then $\sin ^2 \theta+\operatorname{cosec}^2 \theta$ is equal to

(A) 1

(B) 4

(C) 2

(D) None of these

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Best answer

SOLUTION —

On squaring given equation, we get

$\Rightarrow \quad \begin{aligned}\sin ^2 \theta+\operatorname{cosec}^2 \theta+2 & =4 \\\Rightarrow \quad \sin ^2 \theta+\operatorname{cosec}^2 \theta & =2\end{aligned}$

So, The correct option will be (C).

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