Find the principal values of the following questions:
tan−1(−√3)
Let tan−1(−√3)=θ⇒tanθ=−√3
We know that the range of principal value of tan−1 θ is (−π2,π2).
∴ tanθ=−√3=−tanπ3=tan(−π3) (∵ tan(−θ)=−tanθ)
⇒ θ=−π3, where θϵ(−π2,π2)⇒tan−1(−√3)=−π3
Hence, principal value of tan−1(−√3) is −π3