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If $\sin \theta+\operatorname{cosec} \theta=2$, then $\sin ^2 \theta+\operatorname{cosec}^2 \theta=$
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$\begin{aligned}
\sin ^2 \theta+\operatorname{cosec}^2 \theta & =(\sin \theta+\operatorname{cosec} \theta)^2-2 \sin \theta \operatorname{cosec} \theta \\
& =(2)^2-2=4-2=2, \text { since }(\sin \theta+\operatorname{cosec} \theta)=2 .
\end{aligned}$
\sin ^2 \theta+\operatorname{cosec}^2 \theta & =(\sin \theta+\operatorname{cosec} \theta)^2-2 \sin \theta \operatorname{cosec} \theta \\
& =(2)^2-2=4-2=2, \text { since }(\sin \theta+\operatorname{cosec} \theta)=2 .
\end{aligned}$
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