Question:medium
\[
\lim_{x \to 0} \left(\frac{10\sin 9x}{9\sin 10x}\right)
\left(\frac{8\sin 7x}{7\sin 8x}\right)
\left(\frac{6\sin 5x}{5\sin 6x}\right)
\left(\frac{4\sin 3x}{3\sin 4x}\right)
\left(\frac{\sin x}{\sin 2x}\right)
\]
\[
\lim_{x \to 0} \left(\frac{10\sin 9x}{9\sin 10x}\right)
\left(\frac{8\sin 7x}{7\sin 8x}\right)
\left(\frac{6\sin 5x}{5\sin 6x}\right)
\left(\frac{4\sin 3x}{3\sin 4x}\right)
\left(\frac{\sin x}{\sin 2x}\right)
\]
Show Hint
Convert all sine expressions into linear form using \(\sin ax \sim ax\), then simplify systematically.
Updated On: May 8, 2026
- \( \frac{63}{256} \)
- \( \frac{1}{6} \)
- \( \frac{6}{5} \)
- \( \frac{1}{2} \)
- \( \frac{256}{63} \)
Show Solution
The Correct Option is A
Solution and Explanation
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