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Question
Find the principal value of the following:
`tan^-1(1/sqrt3)`
Solution
Let `tan^-1(1/sqrt3) = y`
Then,
`tany=1/sqrt3`
We know that the range of the principal value branch is `(-pi/2,pi/2)`.
Thus,
`tany=1/sqrt3=tan(pi/6)`
`=>y=pi/6in (-pi/2,pi/2)`
Hence, the principal value of `tan^-1(1/sqrt3) is pi/6`
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