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If $\sin \theta+\operatorname{cosec} \theta=2$, then $\sin ^2 \theta+\operatorname{cosec}^2 \theta$ is equal to
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We have $\sin \theta+\operatorname{cosec} \theta=2$
Squaring both the side $\Rightarrow \quad(\sin \theta+\operatorname{cosec} \theta)^2=(2)^2$
$$
\begin{aligned}
&\Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta+2 \sin \theta \cdot \operatorname{cosec} \theta=4 \\
&\Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta+2=4 \Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta=2
\end{aligned}
$$
Squaring both the side $\Rightarrow \quad(\sin \theta+\operatorname{cosec} \theta)^2=(2)^2$
$$
\begin{aligned}
&\Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta+2 \sin \theta \cdot \operatorname{cosec} \theta=4 \\
&\Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta+2=4 \Rightarrow \sin ^2 \theta+\operatorname{cosec}^2 \theta=2
\end{aligned}
$$
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