Mathematics - Inverse Trigonometric Functions Question with Solution | TestHub

${\cot }^{-1}\left(\frac{|\sec 2|-1}{\tan 2}\right)-{\cot }^{-1}\left(\frac{|\sec \frac{1}{2}|+1}{\tan \frac{1}{2}}\right)$
$\begin{array}{rl}& ={\cot }^{-1}\left(\frac{-1-\cos 2}{\sin 2}\right)-{\cot }^{-1}\left(\frac{1+\cos \frac{1}{2}}{\sin \frac{1}{2}}\right)\\ & =\pi -{\cot }^{-1}(\cot 1)-{\cot }^{-1}\left(\cot \frac{1}{4}\right)\\ & =\pi -1-\frac{1}{4}=\pi -\frac{5}{4}\end{array}$