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If $\sin \alpha = \frac{1}{\sqrt{2}}$ and $\cot \beta= \sqrt{3}$, then find the value of $\text{cosec}\alpha+ \text{cosec}\beta$
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$\text{cosec} \alpha = \frac{1}{\sin \alpha} = \sqrt{2}$
$\text{cosec} \beta = \sqrt{1 + \cot^2 \beta} = \sqrt{1+3} = 2$
$\therefore \text{cosec} \alpha + \text{cosec} \beta = \sqrt{2} + 2$ or $\sqrt{2} (\sqrt{2} + 1)$
$\text{cosec} \beta = \sqrt{1 + \cot^2 \beta} = \sqrt{1+3} = 2$
$\therefore \text{cosec} \alpha + \text{cosec} \beta = \sqrt{2} + 2$ or $\sqrt{2} (\sqrt{2} + 1)$