Question

What is the value of \(tan^1⁡\frac{1}{√3}-sin^{-1}⁡1+ cos^{-1}\frac{⁡1}{2}\) is ________

(a) 2π

(b) \(⁡\frac{π}{2}\)

(c) π

(d) 0

This question was posed to me by my college director while I was bunking the class.

Enquiry is from Inverse Trigonometric Functions Basics topic in portion Inverse Trigonometric Functions of Mathematics – Class 12

Answer 1

The correct answer is (c) π

For explanation: \(tan^{-1}⁡\frac{1}{\sqrt{3}}=\frac{π}{6},sin^{-1}⁡1=\frac{π}{2}, cos^{-1}\frac{⁡1}{2}=\frac{π}{3}\)

\(tan^1⁡\frac{1}{\sqrt{3}}-sin^{-1}⁡1+ cos^{-1}⁡\frac{1}{2}=\frac{π}{6}+\frac{π}{2}+\frac{π}{3}=\frac{π+3π+2π}{6}=\frac{6π}{6}=π\)