Q70 / 160 · TS EAMCET 2007 · Mathematics

$\operatorname{sech}^{-1}(\sin \theta)$ is equal to

  • A
    $\log \tan \frac{\theta}{2}$
  • B
    $\log \sin \frac{\theta}{2}$
  • C
    $\log \cos \frac{\theta}{2}$
  • Correct answer
    D
    $\log \cot \frac{\theta}{2}$

Solution

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

Hence, the correct answer is option: 'D'.

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