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Questions  

The value of tan1(tan(6)),is

a
2π-6
b
2π+6
c
6-2π
d
3π-6

detailed solution

Correct option is A

We know that tan−1⁡(tan⁡θ)=θ, if −π2<θ<π2Here, θ=−6 radians which does not lie between −π2 and π2However 2π-6 lies between −π2 and π2 such that    tan⁡(2π−6)=−tan⁡6=tan⁡(−6)∴     tan−1⁡{tan⁡(−6)}=tan−1⁡{tan⁡(2π−6)}=2π−6

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