If $0 < a < 1$, then $\int \frac{d x}{1-2 a \cos x+a^2}=$

• A

  $\frac{1}{1-a^2} \operatorname{Tan}^{-1}\left[\frac{1+a}{1-a} \tan \frac{x}{2}\right]+c$
• B

  $\frac{2}{1+a^2} \operatorname{Tan}^{-1}\left[\frac{1-a}{1+a} \tan \frac{x}{2}\right]+c$
• Correct answer
  C

  $\frac{2}{1-a^2} \operatorname{Tan}^{-1}\left[\frac{1+a}{1-a} \tan \frac{x}{2}\right]+c$
• D

  $\frac{2}{1+a} \operatorname{Tan}^{-1}\left[\frac{1-a^2}{1+a^2} \tan \frac{x}{2}\right]+c$

Hence, the correct answer is option: 'C'.