Simplify the trigonometric expression $\frac{\frac{60}{1-2\cos\left(x\right)}}{\sin\left(x-60\right)}$

$\frac{d}{dx}\left(\frac{\frac{60}{1-2\cos\left(x\right)}}{\sin\left(x-60\right)}\right)=\frac{-60\left(2\sin\left(x\right)\sin\left(x-60\right)+\left(1-2\cos\left(x\right)\right)\cos\left(x-60\right)\right)}{\left(1-2\cos\left(x\right)\right)^2\sin\left(x-60\right)^2}$ See full solution 

$\int\frac{\frac{60}{1-2\cos\left(x\right)}}{\sin\left(x-60\right)}dx=-60\ln\left(\tan\left(\frac{x}{2}\right)\right)+40\ln\left(-\frac{1}{3}+\tan\left(\frac{x}{2}\right)^2\right)+C_0$ See full solution 