Help me to prove this integration Where the method used should be using complex analysis.
$$\int_{c}\frac{d\theta}{(p+\cos\theta)^2}=\frac{2\pi p}{(p^2-1)\sqrt{p^2-1}};c:\left|z\right|=1$$
thanks in advance 

Hint: 
$$\cos \theta = \frac {z + z^{-1}} 2$$
Plug this in and refer to classic tools in complex analysis, such as the Cauchy formula or the residue theorem.
