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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