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Question: A cloud computing consultant models data flow efficiency as $ f(x) = (\sin x + \cos x)^2 + \frac{1}{\sin x \cos x} $, for $ 0 < x < \frac{\pi}{2} $. Find the minimum value of $ f(x) $.
Solution: First, expand $ (\sin x + \cos x)^2 = \sin^2 x + 2\sin x \cos x + \cos^2 x = 1 + 2\sin x \cos x $.
Let $ s = \sin x \cos x $. Then:

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