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Inverse Trigonometric Functions question

2024 · 4 Apr · Shift 2 · Q39

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JEE Main
Mathematics
Inverse Trigonometric Functions
2024 · 4 Apr · Shift 2 · Q39

Inverse Trigonometric Functions question

2024 · 4 Apr · Shift 2 · Q39

JEE MainMathematicsInverse Trigonometric FunctionsMCQ+4 / −1

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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