Let tan(x)=2/5 what is the value of tan(2-x)

Hello from MrBillDoesMath!

-2/5

Discussion:

Generally,

tan(2*PI - x ) = - tanx   =>          (*)

and in our case

tan(2*PI - x ) = - tanx   = - (2/5) = -2/5

Proof of (*)

tan (2*PI-x) = sin (2*Pi-x)/ cos(2*Pi-x)

Now

     sin(2*Pi) * cos(-x) - cos(2*Pi) sin(x) =>  ( sin(2*PI) = 0, cos(2*Pi) = 1)

                     = -sin(x)

     cos(2*Pi-x) =  cos(2*Pi) * cos(-x) + sin(2*Pi)* sin(-x) =>

                            1 * cos(-x)              +  0  =

                            1 * cos(x)  = cos(x)

so tan (2*PI-x) = (-sin(x)) / cos(x) = -tanx

Regards,  

MrB