Q. ${sech}^{- 1}{(\sin\theta)}$ is equal to
A) $\log{\tan\frac{\theta}{2}}$
B) $\log{\sin\frac{\theta}{2}}$
C) $\log{\cos\frac{\theta}{2}}$
D) $\log{\cot\frac{\theta}{2}}$
Explanation
(d)
${sech}^{- 1}\left( \sin\theta \right)$
$= \cosh^{- 1}{(cosec\ \theta)}$
$= \log\left\lbrack cosec\ \theta + \sqrt{\left( {cosec}^{2}\ \theta - 1 \right)} \right\rbrack$
$= \log\left\lbrack \frac{1}{\sin\theta} + \frac{\cos\theta}{\sin\theta} \right\rbrack = \log{\cot\frac{\theta}{2}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.