JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x=A \sqrt{\cos \theta \tan x-\sin \theta}+B \sqrt{\cos \theta-\sin \theta \operatorname{coc} x}+C,\) where \(C\) is the integration constant, then \(A B\) is equal to
- A \(4 \operatorname{cosec}(2 \theta)\)
- B \(4 \sec \theta\)
- C \(2 \sec \theta\)
- D \(8 \operatorname{cosec}(2 \theta)\)
Answer & Solution
Correct Answer
(D) \(8 \operatorname{cosec}(2 \theta)\)
Step-by-step Solution
Detailed explanation
\( \text { Sol. } \int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x \sin (x-\theta)}} d x \) \( I=\int \frac{\sin ^{\frac{3}{2}} x+\cos ^{\frac{3}{2}} x}{\sqrt{\sin ^3 x \cos ^3 x(\sin x \cos \theta-\cos x \sin \theta)}} d x \)…
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