If $A = \begin{bmatrix} \cos x & \sin x \\ -\sin x & \cos x \end{bmatrix}$ and $A + A' = I$, then the value of $x \in \left[-\frac{\pi}{2}, \frac{\pi}{2}\right]$ is:
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For matrix equations like $A+A'=I$, you only need to calculate a single diagonal entry to set up your equation: $a_{11} + a_{11} = 1 \Rightarrow 2\cos x = 1$. This saves time!