The principal value of [\tan ^{-1} \sqrt{3}-\cot ^{-1}(-\sqrt{3})] is

CBSE Class 12 Math 2022 Term I Solved Paper - Question 34

Question : 34 of 50

Marks: +1, -0

The principal value of

[\tan ^{-1} {√{3}}-\cot ^{-1}(-{√{3}})]

Solution:

We have,

\tan ^{-1} {√{3}}-\cot ^{-1}\;(-{√{3}})

\;=\;{π}/{3}- (π-\;{π}/{6})

\;=\tan ^{-1} (\tan \;{π}/{3}) -π+\cot ^{-1} \cot \;{π}/{6}

\;=\;{π}/{3}-\;{5 π}/{6}

\;=-\;{π}/{2}

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