Express the function $f(x)= (1-\sin x)/(1+\sin x)$ as the sum of an even and odd function. Express the function $f(x)= (1-\sin x)/(1+\sin x)$ as the sum of an even and odd function.

$f(x)= \frac{1-\sin x}{1+\sin x} = \frac{(1-\sin x)^2}{(1+\sin x)\times (1-\sin x)} = \frac{1+\sin^2 x-2sinx}{\cos^2 x} = \frac{1}{\cos^2 x}+\tan^2 x  -2 \tan x \sec x  = sec^2 x+\tan^2 x  -2 \tan x \sec x$
Let the even function be $sec^2 x+\tan^2 x $
Let the odd function be $-2 \tan x \sec x $
Because the parity of $\sec^2 x$ and  $\tan^2 x$ and $\tan x$ and $\sec x $, it is easy to verify the parity of the above functions.
