Exercise
$\sqrt{\frac{1-cos\theta\:}{1+cos\theta\:}}$
Derivative of this function
$\frac{d}{dt}\left(\sqrt{\frac{1-\cos\left(t\right)}{1+\cos\left(t\right)}}\right)=\frac{\left(1+\cos\left(t\right)\right)\sin\left(t\right)+\left(1-\cos\left(t\right)\right)\sin\left(t\right)}{2\left(1+\cos\left(t\right)\right)^2}\sqrt{\frac{1+\cos\left(t\right)}{1-\cos\left(t\right)}}$
See step-by-step solution
Integral of this function
$\int\sqrt{\frac{1-\cos\left(t\right)}{1+\cos\left(t\right)}}dt=t\frac{\sqrt{1-\cos\left(t\right)}}{\sqrt{1+\cos\left(t\right)}}+C_0$
See step-by-step solution