]> $$\frac{\partial }{\partial x}\frac{\cos {}^k\left(\theta \right)}{{\sin }^n\left(\theta \right)}=\frac{1}{{\sin }^{n+1}\left(\theta \right)}\left(\left(k-n\right){\cos }^{n+1}\left(\theta \right)-k{\cos }^{n-1}\left(\theta \right)\right)$$