What is the value of `sin^(-1)("sin"(2 pi)/(3))` ?

Options

A. `-(pi)/(3)`
B. `(2 pi)/(3)`
C. `-(2 pi)/(3)`
D. `(pi)/(3)`

Answer

D

Explanation

`sin^(-1)("sin"(2pi)/(3))=sin^(-1)[sin(pi-(2pi)/(3))]=sin^(-1)("sin"(pi)/(3))=(pi)/(3)" "["since, sin"(2pi)/(3)=sin(pi-(pi)/(3))]`