$\mathrm{A}=\left[\begin{array}{cc}0& -\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\\ \tan {\displaystyle \frac{\mathrm{\alpha }}{2}}& 0\end{array}\right]$

$\therefore \mathrm{I}+\mathrm{A}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]+\left[\begin{array}{cc}0& -\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\\ \tan {\displaystyle \frac{\mathrm{\alpha }}{2}}& 0\end{array}\right]$

$=\left[\begin{array}{cc}1& \tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\\ \tan {\displaystyle \frac{\mathrm{\alpha }}{2}}& 1\end{array}\right]$

$\therefore \mathrm{I}-\mathrm{A}=\left[\begin{array}{cc}1& \tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\\ -\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}& 1\end{array}\right]$

$\therefore (\mathrm{I}-\mathrm{A})\left[\begin{array}{cc}\cos \mathrm{\alpha }& \sin \mathrm{\alpha }\\ \sin \mathrm{\alpha }& \cos \mathrm{\alpha }\end{array}\right]=\left[\begin{array}{cc}1& \tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\\ -\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}& 1\end{array}\right]\left[\begin{array}{cc}\cos \mathrm{\alpha }& \sin \mathrm{\alpha }\\ \sin \mathrm{\alpha }& \cos \mathrm{\alpha }\end{array}\right]$

$=\left[\begin{array}{cc}\cos \mathrm{\alpha }+\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\sin \mathrm{x}& \sin \mathrm{\alpha }+\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\cos \mathrm{\alpha }\\ -\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\cos {\mathrm{\alpha }}^2+\sin \mathrm{\alpha }& -\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\sin +\cos \mathrm{\alpha }\end{array}\right]$

$=\left[\begin{array}{cc}1& -\tan {\displaystyle \frac{\mathrm{\alpha }}{2}}\\ \tan {\displaystyle \frac{\mathrm{\alpha }}{2}}& 1\end{array}\right]$