Question

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) 0

The 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 1

Right answer is (c) \(\frac{1}{2}\)

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

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

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