MathematicsMedium66×since 2002Q4082Given that the inverse trigonometric function assumes principal values only. Let x,yx, yx,y be any two real numbers in [−1,1][-1,1][−1,1] such that cos−1x−sin−1y=α,−π2≤α≤π\cos ^{-1} x-\sin ^{-1} y=\alpha, \frac{-\pi}{2} \leq \alpha \leq \picos−1x−sin−1y=α,2−π≤α≤π. Then, the minimum value of x2+y2+2xysinαx^2+y^2+2 x y \sin \alphax2+y2+2xysinα isA0B−-−1C12\frac{1}{2}21D−12\frac{-1}{2}2−1Check answerSkip