JEE Math Practice Question
Given that the inverse trigonometric function assumes principal values only. Let $$x, y$$ be any two real numbers in $$[-1,1]$$ such that $$\cos ^{-1} x-\sin ^{-1} y=\alpha, \frac{-\pi}{2} \leq \alpha \leq \pi$$. Then, the minimum value of $$x^2+y^2+2 x y \sin \alpha$$ is
- A.0
- B.$$-$$1
- C.$$\frac{1}{2}$$
- D.$$\frac{-1}{2}$$
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