coty = x - y
i worked it to...
dy/dx = 1/(1-csc球)
Your answer is correct
You could simplify your denominator
$\displaystyle \frac{1}{1-\csc^2y}=\frac{1}{-\cot^2y}=-\tan^2y$
ab + b = b(a + 1)
$\displaystyle -\csc ^2y\, \frac{dy}{dx} + \frac{dy}{dx} =1$
$\displaystyle \frac{dy}{dx}\,(- \csc ^2y+1)=1$
$\displaystyle \frac{dy}{dx}=\frac{1}{- \csc ^2y+1}$