The value of tan−1(tan(−6)),is
2π-6
2π+6
6-2π
3π-6
We know that tan−1(tanθ)=θ, if −π2<θ<π2
Here, θ=−6 radians which does not lie between −π2 and π2
However 2π-6 lies between −π2 and π2 such that
tan(2π−6)=−tan6=tan(−6)∴ tan−1{tan(−6)}=tan−1{tan(2π−6)}=2π−6