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Question
Find the principal value of the following:
tan−1 (−1)
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Solution
Let tan−1 (−1) = y
Then tan y = −1 = `-tan (pi/2) = tan (-pi/2)`
We know that the range of the principal value branch of tan−1 is `(-pi/2, pi/2)` and `tan(-pi/4) = - 1`.
Where `-pi/4 ∈ (-pi/2, pi/2)`
Therefore, the principal value of tan−1 (−1) is `pi/4`.
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