Minimum & Maximum

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.