What is the <strong>MINIMUM</strong> value of \frac{\sin^{2}A+5 \sin A+1}{\sin A} for 0 \lt A \leq \frac{\pi}{2} ?

Explanation

The expression simplifies to \sin A + \frac{1}{\sin A} + 5. For A \in (0, \pi/2], \sin A is in (0, 1]. The function x + 1/x for x \in (0, 1] attains its minimum at x = 1. Thus, the minimum value is 1 + 1 + 5 = 7.

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