Question

f(u) = 2tan^-1 ( e^u) check wheather it is even function , odd or neither ?

Answer 1

@shubhamsrg @sirm3d

Answer 2

the function is odd

Answer 3

f(u) = tan-1 ( 2e^u /1-e^u)
f(-u) = tan-1 (2 e^u/1-e^u)

hence func is even

Answer 4

@shubhamsrg the function shuld be odd...but i dont kow hw ???

Answer 5

@electrokid

Answer 6

notice that: \[\tan\theta=e^u=\frac{\sin\theta}{\cos\theta}\\
e^{-u}=\cot\theta\implies\tan^{-1}(e^{-u})=-\theta\]

Answer 7

so,
\[f(u)=2\tan^{-1}(e^u)=2\theta\\\implies f(-u)=2\tan^{-1}(e^{-u})=-2\theta\\\implies f(-u)=-f(u)\]

Answer 8

oops, I made blunder in my calculations, yes its odd.