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$\operatorname{sech}^{-1}(\sin \theta)$ is equal to
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The correct answer is:
$\log \cot \frac{\theta}{2}$
We have, sech ${ }^{-1}(\sin \theta)$
$\begin{aligned} & =\cos h^{-1}(\operatorname{cosec} \theta) \\ & =\log \left[\operatorname{cosec} \theta+\sqrt{\left(\operatorname{cosec}^2 \theta-1\right)}\right] \\ & =\log \cot \frac{\theta}{2}\end{aligned}$
$\begin{aligned} & =\cos h^{-1}(\operatorname{cosec} \theta) \\ & =\log \left[\operatorname{cosec} \theta+\sqrt{\left(\operatorname{cosec}^2 \theta-1\right)}\right] \\ & =\log \cot \frac{\theta}{2}\end{aligned}$
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