Question

If $A=\left[\begin{array}{cc}1& tan\frac{\theta }{2}\\ -tan\frac{\theta }{2}& 1\end{array}\right]$ and AB = I, then B =

• A. $co{s}^2\frac{\theta }{2}.A$
• B. $co{s}^2\frac{\theta }{2}.A^T$
• C. $co{s}^2\frac{\theta }{2}.I$
• D. $\text{None of these}$

Answer 1

The correct option is B $co{s}^2\frac{\theta }{2}.A^T$

$|A|=1+ta{n}^2\frac{\theta }{2}=se{c}^2\frac{\theta }{2}AB=I\Rightarrow B-I{A}^{-1}\frac{\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]\left[\begin{array}{cc}1& -tan\frac{\theta }{2}\\ tan\frac{\theta }{2}& 1\end{array}\right]}{se{c}^2\frac{\theta }{2}}=co{s}^2\frac{\theta }{2}.A^T.$