Mathematics - Trigonometric Ratios & Identities Question with Solution | TestHub

${\text{sec}}^{-1}\left[\frac{1}{4}\sum _{k=0}^{10}\sec \left(\frac{7\pi }{12}+\frac{k\pi }{2}\right)\sec \left(\frac{7\pi }{12}+\frac{k\pi }{2}+\frac{\pi }{2}\right)\right]$
$\begin{array}{cc}={\text{sec}}^{-1}\left[\frac{-1}{4}\sum _{k=0}^{10}\sec \left(\frac{7\pi }{12}+\frac{k\pi }{2}\right)\text{cosec}\left(\frac{7\pi }{12}+\frac{k\pi }{2}\right)\right]& \left(\therefore \sec \left(\frac{\pi }{2}+\theta \right)=-\text{cosec}\theta \right)\end{array}$


now if
and if
hence

$={\sec }^{-1}1$
$=0$