Find the principal values of the following questions:

$c o t^{- 1} (\sqrt{3})$

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Solution

Let $c o t^{- 1} (\sqrt{3}) = θ \Rightarrow c o t θ = \sqrt{3}$
We know that the range of principal value of $c o t^{- 1} (\sqrt{3}) = \frac{π}{6}$
$∴ c o t θ = \sqrt{3} = c o t \frac{π}{6} \Rightarrow θ = \frac{π}{6}$ ; where $θ ϵ (0, π) \Rightarrow c o t^{- 1} (\sqrt{3}) = \frac{π}{6}$
Hence, the principal value of $c o t^{- 1} (\sqrt{3})$ is $\frac{π}{6}$

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