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Question
Find the value of `tan^-1 (tan (2pi)/3)`
Solution
We know that `(2pi)/3 ∉ [(-pi)/2, pi/2]`
∴ `tan^-1(tan (2pi)/3) = tan^-1[tan(pi - pi/3)]`
= `tan^-1(- tan pi/3)`
= `- tan^-1(tan pi/3)` ......`[because tan^-1(- x) = - tan^-1x]`
= `- pi/3 ∈ [-pi/2, pi/2]`
Hence, `tan^-1 (tan (2pi)/3) = (-pi)/3`.
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