1 cos theta-sin^ theta/sin theta(1 + cos theta) = cot theta

If you bothered to check the equation that you wrote you would see that it doesn't make much sense. You can't copy and paste math equations from other applications into this forum, and further you need to include parentheses so we can tell what it is that you are asking. However, I'm guessing what you meant to write is this:

(1+cos(theta)-sin^2(theta))/(sin(theta) x (1 + cos(theta))) = cot(theta)

Hint: multiply numerator and denominator by (1-cos(theta)), and it works right out.