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

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Answer 1 · 2017-11-01T10:52:04

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

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.

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