Question

$\left[\begin{array}{cc}1& -\tan \alpha /2\\ \tan \alpha /2& 1\end{array}\right]\left[\begin{array}{cc}\tan \alpha /2& 1\\ 1& 0\end{array}\right]$ equals-

• A. zero matirx
• B. ${\sec }^2\alpha .I_2$
• C. $I_2$
• D. None of these

Answer 1

The correct option is D None of these

$\left[\begin{array}{cc}1& -\tan \frac{\alpha }{2}\\ \tan \frac{\alpha }{2}& 1\end{array}\right]\left[\begin{array}{cc}\tan \frac{\alpha }{2}& 1\\ 1& 0\end{array}\right]$
$=\left[\begin{array}{cc}\tan \frac{\alpha }{2}-\tan \frac{\alpha }{2}& 1\\ 1+{\tan }^2\frac{\alpha }{2}& \tan \frac{\alpha }{2}\end{array}\right]$
$=\left[\begin{array}{cc}0& 1\\ {\sec }^2\frac{\alpha }{2}& \tan c\frac{\alpha }{2}\end{array}\right]=-{\sec }^2\frac{\alpha }{2}$