The question is $ \displaystyle \int{ \frac{1-r^{2}}{1-2r\cos(\theta)+r^{2}}} d\theta$.
I know it will be used weierstrass substitution to solve but i did not have any idea of it.
The question is $ \displaystyle \int{ \frac{1-r^{2}}{1-2r\cos(\theta)+r^{2}}} d\theta$.
I know it will be used weierstrass substitution to solve but i did not have any idea of it.
Apply the substitution $\tan \frac{\theta}{2}=t.$ Then use $\cos\theta=\frac{1-t^2}{1+t^2}$.
There's a Wikipedia article about this technique: Weierstrass substitution.
Notice that what you've got here is $\displaystyle\int\frac{d\theta}{a+b\cos\theta}$. The factor $1-r^2$ pulls out, and $a=1+r^2$ and $b=-2r$.