Question 1028543
<pre>
{{{1/(sec(x)+tan(x))= sec(x)-tan(x)}}}

Work with the left side only:

{{{(1/(sec(x)+tan(x)))((sec(x)-tan(x))/(sec(x)-tan(x)))}}}

{{{(sec(x)-tan(x))/(sec^2(x)-tan^2(x))}}}

{{{(sec(x)-tan(x))/1}}}

{{{sec(x)-tan(x)}}}

Edwin</pre>