The value of `sin^(-1)`(sin 10) is

Options

A. `3pi-10`
B. `10-3pi`
C. `3pi+10`
D. `4pi-10`

Answer

A

Explanation

We know that `sin^(-1)(sin theta)=theta if -(pi)/(2)letheta le(pi)/(2)`
Here `theta =10` radians which does not lie between `-(pi)/(2) and (pi)/(2)`
But `3pi-theta` lies between `-(pi)/(2)and (pi)/(2)`
also `sin(3pi-10)=sin10`
`therefore sin^(-1)(sin10)=sin^(-1)sin(3pi-10)=3pi-10`