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If \(\sin (\theta)+\operatorname{cosec}(\theta)=2\), then \(\sin ^{2020}(\theta)+\operatorname{cosec}^{2020}(\theta)=\ldots\).
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\(\sin \theta+\operatorname{cosec} \theta=2\)
\(\Rightarrow \quad \sin \theta+\frac{1}{\sin \theta}=2 \Rightarrow(\sin \theta=1)\)
So, \(\quad \sin ^{2020} \theta+\cos ^{2020} \theta=1+1=2\)
\(\Rightarrow \quad \sin \theta+\frac{1}{\sin \theta}=2 \Rightarrow(\sin \theta=1)\)
So, \(\quad \sin ^{2020} \theta+\cos ^{2020} \theta=1+1=2\)
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