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Find the value of \(cos⁡(sin^{-1}⁡\frac{\sqrt{3}}{2})\) is _____(a) \(\frac{\sqrt{3}}{2}\)(b) \(\frac{1}{4}\)(c) \(\frac{1}{2}\)(d) 0The question was posed to me during an interview.This intriguing question comes from Inverse Trigonometric Functions Basics in chapter Inverse Trigonometric Functions of Mathematics – Class 12

Answer» RIGHT answer is (C) \(\frac{1}{2}\)

For explanation I would SAY: \(sin⁡\frac{π}{3}=\frac{\sqrt{3}}{2}\)

∴\(sin^{-1}⁡\frac{\sqrt{3}}{2}=\frac{π}{3}\)

⇒\(cos⁡(sin^{-1}⁡\frac{\sqrt{3}}{2})=cos⁡(\frac{π}{3})=\frac{1}{2}\).


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