Question:
\(\int \frac{\sin 4\theta}{\sin 2\theta} \, d\theta =\)
\(\int \frac{\sin 4\theta}{\sin 2\theta} \, d\theta =\)
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\(\sin 2x = 2\sin x \cos x\) and \(\sin 4x = 2\sin 2x \cos 2x\).
Updated On: Apr 24, 2026
- \(\frac{\sin \theta}{2} + C\)
- \(\cos 2\theta + C\)
- \(2\sin 2\theta + C\)
- \(\frac{\cos \theta}{2} + C\)
- \(\sin 2\theta + C\)
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The Correct Option is
Solution and Explanation
Step 1: Understanding the Concept:
Use the identity \(\sin 4\theta = 2\sin 2\theta \cos 2\theta\).
Step 2: Detailed Explanation:
\(\frac{\sin 4\theta}{\sin 2\theta} = \frac{2\sin 2\theta \cos 2\theta}{\sin 2\theta} = 2\cos 2\theta\)
\(\int 2\cos 2\theta \, d\theta = 2 \cdot \frac{\sin 2\theta}{2} + C = \sin 2\theta + C\)
Step 3: Final Answer:
\(\sin 2\theta + C\).
Use the identity \(\sin 4\theta = 2\sin 2\theta \cos 2\theta\).
Step 2: Detailed Explanation:
\(\frac{\sin 4\theta}{\sin 2\theta} = \frac{2\sin 2\theta \cos 2\theta}{\sin 2\theta} = 2\cos 2\theta\)
\(\int 2\cos 2\theta \, d\theta = 2 \cdot \frac{\sin 2\theta}{2} + C = \sin 2\theta + C\)
Step 3: Final Answer:
\(\sin 2\theta + C\).
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