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$$A_x = \begin{bmatrix}\sin x & -\cos x \\\cos x & \sin x \end{bmatrix} \Rightarrow \sin x.A_x + \cos x.A_{\left(\frac{\pi}{2} + x\right)} =$$
$$\left(\begin{array}{c}1 & -1\\ -1 & 0\end{array}\right)$$
$$\left(\begin{array}{c}0 & 1\\ 1 & 0\end{array}\right)$$
$$\left(\begin{array}{c}1 & 1\\ 1 & 1\end{array}\right)$$
$$\left(\begin{array}{c}1 & 0\\ 0 & 1\end{array}\right)$$
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