MathematicsHard64×since 2004Q4038If ∫sin32x+cos32xsin3xcos3xsin(x−θ)dx=Acosθtanx−sinθ+Bcosθ−sinθcotx+C\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\cos \theta \tan x-\sin \theta}+B \sqrt{\cos \theta-\sin \theta \cot x}+C∫sin3xcos3xsin(x−θ)sin23x+cos23xdx=Acosθtanx−sinθ+Bcosθ−sinθcotx+C, where CCC is the integration constant, then ABA BAB is equal toA2secθ2 \sec \theta2secθB8cosec(2θ)8 \operatorname{cosec}(2 \theta)8cosec(2θ)C4cosec(2θ)4 \operatorname{cosec}(2 \theta)4cosec(2θ)D4secθ4 \sec \theta4secθCheck answerSkip