JEE Mains · Maths · STD 12 - 7.1 indefinite integral
If \(\int \frac{\cos \theta}{5+7 \sin \theta-2 \cos ^{2} \theta} d \theta=A \log _{e}|B(\theta)|+C\) where \(C\) is a constant of integration, then \(\frac{ B (\theta)}{ A }\) can be
- A \(\frac{2 \sin \theta+1}{5(\sin \theta+3)}\)
- B \(\frac{2 \sin \theta+1}{\sin \theta+3}\)
- C \(\frac{5(\sin \theta+3)}{2 \sin \theta+1}\)
- D \(\frac{5(2 \sin \theta+1)}{\sin \theta+3}\)
Answer & Solution
Correct Answer
(D) \(\frac{5(2 \sin \theta+1)}{\sin \theta+3}\)
Step-by-step Solution
Detailed explanation
\(\int \frac{\cos \theta d \theta}{5+7 \sin \theta-2 \cos ^{2} \theta}\) \(\int \frac{\cos \theta d \theta}{3+7 \sin \theta+2 \sin ^{2} \theta} \quad \mid \begin{array}{l}\sin \theta=t \\ \cos \theta d \theta= dt \end{array}\)…
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