If cos^-1 x - sin^-1 y = α x, y ∈ (-1, 1) If α ∈ [-π/2 , π] Then minimum value of x^2 + y^2 + 2xy sinα is

Question

If  \(cos ^{-1}x - sin ^{-1} y = \alpha\) 

\(x,y \in (-1,1)\)

If \(\alpha \in \left[\frac {-\pi}{2}, \pi\right]\)

Then minimum value of x² + y² + 2xy sinα is

(1) \(\frac {-1}{2}\)

(2) -1 

(3) 1/2 

(4) 0

Answer 1

Correct option is (4) 0

Now min value of E is 0