Minimum & Maximum

Geometry Level 4

For a fixed value of \(\alpha\), the minimum and maximum values of the expression \(y = \cos\theta\left( \sin\theta + \sqrt{\sin^2\theta + \sin^2\alpha } \right) \) are:

A: \( -\sqrt{1 - \sin^2\alpha} \) and \( \sqrt{1 - \sin^2\alpha}\).
B. \( -\sqrt{1 + \sin^2\alpha} \) and \(\sqrt{1+\sin^2\alpha} \).
C. \(1 - \sqrt{1+\sin^2\alpha} \) and \(1 + \sqrt{1 + \sin^2\alpha} \).
D. None of these choices.

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