MathematicsMedium64×since 2004Q4057If ∫1a2sin2x+b2cos2x dx=112tan−1(3tanx)+\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)+∫a2sin2x+b2cos2x1 dx=121tan−1(3tanx)+ constant, then the maximum value of asinx+bcosx\mathrm{a} \sin x+\mathrm{b} \cos xasinx+bcosx, is :A41\sqrt{41}41B39\sqrt{39}39C40\sqrt{40}40D42\sqrt{42}42Check answerSkip