(i) Let
![\[\begin{array}{*{35}{l}} y\text{ }=\text{ }co{{t}^{-1}}\left( -\surd 3 \right) \\ \text{ }Cot\text{ }\left( \pi /6 \right)\text{ }=\text{ }\surd 3 \\ =\text{ }Cot\text{ }\left( \pi \text{ }\text{ }-\pi /6 \right) \\ =\text{ }cot\text{ }\left( 5\pi /6 \right) \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-57f760fdf53a42a1e7325f28d4628cbd_l3.png "Rendered by QuickLaTeX.com")
The range of principal value of cot-1 is (0, π) and cot (5 π/6) = – √3
=> the principal value of cot-1 (- √3) is 5π/6
(ii) Let
![\[\begin{array}{*{35}{l}} y\text{ }=\text{ }co{{t}^{-1}}\left( \surd 3 \right) \\ Cot\text{ }\left( \pi /6 \right)\text{ }=\text{ }\surd 3 \\ \end{array}\]](https://www.learnatnoon.com/s/wp-content/ql-cache/quicklatex.com-9f031984daf5ab58e4ba18a643bece1c_l3.png "Rendered by QuickLaTeX.com")
The range of principal value of cot-1 is (0, π) and
=> the principal value of cot-1 (√3) is π/6
Find the principal values of each of the following:(i) 
(ii) 
(ii) Find the principal values of each of the following:(i) (ii)
(ii)