5Question: Find the minimum value of $(\cos x + \sec x)^2 + (\sin x + \csc x)^2$ for $0 < x < \frac{\pi}{2}$.
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- We begin by expanding the expression:
- Recall that $\cos x \sec x = 1$ and $\sin x \csc x = 1$, so the expression becomes:
- \cos^2 x + \sin^2 x + 2 + \sec^2 x + \csc^2 x + 2
