If \(\int \frac{1}{a^{2} \sin ^{2} x+b^{2} \cos ^{2} x} d x=\frac{1}{18} \tan ^{-1}(2 \tan x)+C\), then the maximum value of a sinx + b cosx is

1
5√3
2
3√5
3
√5
4
√3

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