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Considering the principal values of the inverse trigonometric functions, \({\sin }^{-1}\left(\frac{\sqrt{3}}{2}x+\frac{1…

Q1

Considering the principal values of the inverse trigonometric functions, \({\sin }^{-1}\left(\frac{\sqrt{3}}{2}x+\frac{1}{2}\sqrt{1-{x}^{2}}\right),-\frac{1}{2}

[JEE Main 2025, 4 Apr (Shift 1)]

a

\(\frac{\pi }{4}+{\sin }^{-1}x\)

b

\(\frac{\pi }{6}+{\sin }^{-1}x\)

c

\(\frac{-5\pi }{6}-{\sin }^{-1}x\)

d

\(\frac{5\pi }{6}-{\sin }^{-1}x\)

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