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Question
Find the principal value of tan−1 (−1)
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`
Whare `-pi/4 ∈ (-pi/2, pi/2)`
Therefore, the principal value of `tan^(-1) (-1) " is " pi/4.`
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