Compute the following $(iv)\;\begin{bmatrix}\cos^2x & \sin^2x\\ \sin^2x & \cos^2x\end{bmatrix}+\begin{bmatrix}\sin^2x & \cos^2x\\ \cos^2x & \sin^2x\end{bmatrix}$

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Note: This is the 4th part of a 4 part question, which is split as 4 separate questions here.