Given 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 \text{. } Then, the minimum value of x^2+y^2+2 x y \sin \alpha is [4 Apr 2024 Shift 2]

Inverse Trigonometric Functions

Section: Mathematics

Question : 20 of 95

Marks: +1, -0

Given the inverse trigonometric function assumes principal values only. Let x,y be any two real numbers in [−1,1] such that
cos−1x−sin‌−1y=α,‌

−π

≤α≤π‌. ‌
Then, the minimum value of x2+y2+2xysin‌α is

[4 Apr 2024 Shift 2]

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