If ∫ (sin^(3/2)x + cos^(3/2)x)/√(sin³ x cos³ x sin(x-θ)) dx = A√(… | JEE Main 2024 Mathematics PYQ

MCQMediumJEE Main 2024 · 29 January, Shift 2Indefinite Integrals

If $\int \frac{\sin^{3/2}x + \cos^{3/2}x}{\sqrt{\sin^3 x \, \cos^3 x \, \sin(x-\theta)}} \, dx = A\sqrt{\cos\theta \tan x - \sin\theta} + B\sqrt{\cos\theta - \sin\theta \cot x} + C$ , where $C$ is the integration constant, then $AB$ is equal to:

A
$4 \csc(2\theta)$
B
$4 \sec \theta$
C
$2 \sec \theta$
D
$8 \csc(2\theta)$

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