$\begin{align*} \int \frac{dx}{a^2 \sin^2x +b^2 \cos^2 x} \end{align*}$ is equal to :

Question

( A ) $\tan^{-1} \begin{pmatrix} \frac{a \tan x}{b} \end{pmatrix} + c$
( B ) $\frac{1}{ab} \tan^{-1} \begin{pmatrix} \frac{b \tan x}{a} \end{pmatrix} + c$
( C ) $\tan^{-1} \begin{pmatrix} \frac{b \tan x}{a} \end{pmatrix} + c$
( D ) $\frac{1}{ab} \tan^{-1} \begin{pmatrix} \frac{a \tan x}{b} \end{pmatrix} + c$