Question 632972
<pre>
{{{(tan^2(x) - cot^2(x)) /(tan(x) + cot(x))}}} = tan(x) - cot(x)

The numerator of the left is the difference of squares.

It can be factored just like AČ - BČ = (A - B)(A + B)


{{{((tan(x) - cot(x))(tan(x) + cot(x))) /(tan(x) + cot(x))}}}

Then we just cancel the (tan(x) + cot(x))'s

{{{((tan(x) - cot(x))cross((tan(x) + cot(x)))) /cross((tan(x) + cot(x)))}}}

and all that's left is

tan(x) - cot(x)

Edwin</pre>