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[tex]\lim_{x \to 0} \frac{cosec6x}{cosec12x} \\\\= \lim_{x \to 0} \frac{\frac{1}{sin6x} }{\frac{1}{sin12x} } \\\\= \lim_{x \to 0} \frac{sin12x}{sin6x} \\\\= \lim_{x \to 0} \frac{sin2(6x)}{sin6x} \\\\= \lim_{x \to 0} \frac{2\ sin6x\ cos6x}{sin6x} \\\\= \lim_{x \to 0} 2cos6x\\\\=2cos6(0)\\\\=2cos0\\\\=2(1)\\\\=2[/tex]
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