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Question
Find the principal value of the following:
tan-1 (-1)
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Solution
tan-1 (-1) = y
(-1) = tan y where `(-pi)/2 <= y <= pi/2`
(or) tan y = – 1
tan y = tan`(- pi/4) (because tan pi/4 = 1)`
∴ y = `- pi/4 [because tan(- pi/4) = - tan(pi/4) = - 1]`
∴ The principal value of tan-1 (-1) is `- pi/4`.
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