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Question
Find the principal value of `tan^(-1) (-sqrt3)`
Solution
Let `tan^(-1) (-sqrt(3))` = y
Then tan y = `-sqrt(3) = -tan pi/3 = tan (-pi/3)`
We know that the range of the principal value branch of tan−1x is
`(-pi/2, pi/2)` and `tan(-pi/3)` are `-sqrt(3)`
Therefore, the principal value of `tan^(-1) (-sqrt3)` is `- pi/3`
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