`sin [ cos^(-1) (-(1)/(2))]` का मान निकालें|

Options

A. ` (sqrt(3))/(2)`
B. ` sqrt(3)`
C. ` -(sqrt(3))/(2)`
D. 0

Answer

A

Explanation

`= sin""(pi)/(3)-(-(pi)/(3))] = sin[(pi)/(3) + (pi)/(6)] = sin""(pi)/(2) =1`
`= sin[pi - cos^(-1)""(1)/(2)] " "[because cos^(-1)(-(1)/(2)) = pi-cos^(-1)""(1)/(2)]`
`= sin [pi-(pi)/(3) ] = sin ""(2pi)/(3) = (sqrt(3))/(2) " "[because cos^(-1)((1)/(2)) = (pi)/(3)]`