Question

What kind of function is `f(x)=log((1+sinx)/(1-sinx))`? Whether odd, even or none?

Answer 1

`f(x)=log((1+sinx)/(1-sinx))` is an odd function.

Explanation:

A function is even if `f(-x)=f(x)`

and it is odd if `f(-x)=-f(x)`

here we have `f(x)=log((1+sinx)/(1-sinx))=log(1+sinx)-log(1-sinx)`#

Hence `f(-x)=log((1+sin(-x))/(1-sin(-x)))`

= `log((1-sinx)/(1+sinx))` - (as `sin(-x)=-sinx`)

= `log(1-sinx)-log(1+sinx)`

= `-f(x)`

Hence `f(x)=log((1+sinx)/(1-sinx))` is an odd function.