Mathematics · 2024
JEE Main · 29 January 2024, Shift 2 · Q10
If ∫ (sin^(3/2) x+ cos^(3/2) x)/(√(sin^3 x cos^3 x sin (x-θ))) d x=A √(cos θ tan x- sin θ)+B √(cos θ- sin θ cot x)+C, where C is the integration…
If $\displaystyle \int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\cos \theta \tan x-\sin \theta}+B \sqrt{\cos \theta-\sin \theta \cot x}+C$, where $\displaystyle C$ is the integration constant, then $\displaystyle A B$ is equal to
Official answer
From NTA’s final answer key for this paper.
(1)
$\displaystyle 8 \operatorname{cosec}(2 \theta)$
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JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.