Question:
$\int\frac{\sin 2x}{\sin x}dx=$ ________.
$\int\frac{\sin 2x}{\sin x}dx=$ ________.
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Always simplify trigonometric fractions before integrating.
Updated On: Jun 26, 2026
- $\sin x+C$
- $2 \cos x+C$
- $-\cos x+C$
- $-\sin x+C$
- $2 \sin x+C$
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The Correct Option is
Solution and Explanation
Step 1: Concept
Use the trigonometric identity $\sin 2x = 2 \sin x \cos x$.
Step 2: Meaning
The integral becomes $\int \frac{2 \sin x \cos x}{\sin x} dx$.
Step 3: Analysis
Cancel $\sin x$: $\int 2 \cos x dx$.
Step 4: Conclusion
$2 \int \cos x dx = 2 \sin x + C$. Final Answer: (E)
Use the trigonometric identity $\sin 2x = 2 \sin x \cos x$.
Step 2: Meaning
The integral becomes $\int \frac{2 \sin x \cos x}{\sin x} dx$.
Step 3: Analysis
Cancel $\sin x$: $\int 2 \cos x dx$.
Step 4: Conclusion
$2 \int \cos x dx = 2 \sin x + C$. Final Answer: (E)
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