Find the principal value of each of the following:\(tan^{-1}(\frac{1}{

1.	Find the principal value of each of the following:\(tan^{-1}(\frac{1}{\sqrt3})\)
Answer» We know that, for any x ∈ R, tan^-1represent an angle in \((\frac{-\pi}2,\frac{\pi}2)\) whose tangent is x. So, \(tan^{-1}(\frac{1}{\sqrt3})\) = An angle in \((\frac{-\pi}2,\frac{\pi}2)\) whose tangent is \(\frac{1}{\sqrt3}\) \(=-\frac{\pi}6\) \(\therefore\,tan^{-1}(\frac{1}{\sqrt3})=-\frac{\pi}6\) Hence, Principal value of tan^-1\((\frac{1}{\sqrt3})\) is \(-\frac{\pi}6\).

Find the principal value of each of the following:\(tan^{-1}(\frac{1}{\sqrt3})\)

Answer»

We know that, for any x ∈ R, tan^-1represent an angle in \((\frac{-\pi}2,\frac{\pi}2)\) whose tangent is x.

So, \(tan^{-1}(\frac{1}{\sqrt3})\) = An angle in \((\frac{-\pi}2,\frac{\pi}2)\) whose tangent is \(\frac{1}{\sqrt3}\)

\(=-\frac{\pi}6\)

\(\therefore\,tan^{-1}(\frac{1}{\sqrt3})=-\frac{\pi}6\)

Hence, Principal value of tan^-1\((\frac{1}{\sqrt3})\) is \(-\frac{\pi}6\).