arctan(tan7)=2pi-7why??i m confused....

the range of the arctan function is (-π/2,π/2)

in addition, tan(theta)=nπ+ (-1)ⁿarctan(theta), where 'n' is any integer.

Hi Shreya,

Please note that tan^-1t has range between -Π/2 and +Π/2.

So tan^-1tanx = x ----------- when -Π/2 < x < +Π/2-------(1)

So tan^-1tan7 = tan^-1(-tan(2Π-7) = tan^-1tan(7-2Π)-------- {Now note 7-2Π lies in the given interval of (1)}.

And hence the answe is 7-2Π, and it is not 2Π-7.

Hope that helps.

All the best,

Regards,

Ashwin (IIT Madras)