Question

Compute $\left[\begin{array}{cc}{\cos }^{2}x& {\sin }^{2}x\\ {\sin }^{2}x& {\cos }^{2}x\end{array}\right]+\left[\begin{array}{cc}{\sin }^{2}x& {\cos }^{2}x\\ {\cos }^{2}x& {\sin }^{2}x\end{array}\right]$

Answer 1

$\left(\begin{array}{cc}{\cos }^{2}x& {\sin }^{2}x\\ {\sin }^{2}x& {\cos }^{2}x\end{array}\right)+\left(\begin{array}{cc}{\sin }^{2}x& {\cos }^{2}x\\ {\cos }^{2}x& {\sin }^{2}x\end{array}\right)$

$\begin{array}{c}\left[\begin{array}{cc}{\cos }^{2}x+{\sin }^{2}x& {\sin }^{2}x+{\cos }^{2}x\\ {\sin }^{2}x+{\cos }^{2}x& {\cos }^{2}x+{\sin }^{2}x\end{array}\right]\\ =\left[\begin{array}{cc}1& 1\\ 1& 1\end{array}\right]\end{array}$

$\left({\sin }^2\theta +{\cos }^2\theta =1\right)$