Question 826390
You're going to laugh (or cry) when you see how close you were:
{{{(cos(x)-cos^2(x))/(sin(x)-sin(x)cos(x))}}}
We're going to reduce this fraction. And since only factors cancel, we will factor the numerator and denominator:
{{{(cos(x)(1-cos(x)))/(sin(x)(1-cos(x)))}}}
And, as we can see, a factor will cancel:
{{{(cos(x)cross((1-cos(x))))/(sin(x)cross((1-cos(x))))}}}
leaving
{{{cos(x)/sin(x)}}}
which is equal to:
{{{cot(x)}}}