Indefinite Integrals

If \(\int \frac{1}{\mathrm{a}^2 \sin ^2 x+\mathrm{b}^2 \cos ^2 x} \mathrm{~d} x=\frac{1}{12} \tan ^{-1}(3 \tan x)+\) constant, then the maximum value of \(\mathrm{a} \sin x+\mathrm{b} \cos x\), is :