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Home  >>  JEEMAIN and AIPMT  >>  Mathematics  >>  Trignometry
0 votes

$\sin\large\frac{9\pi}{14}$$\sin\large\frac{11\pi}{14}$$\sin\large\frac{13\pi}{14}$ is equal to

$(a)\;\large\frac{1}{64}$$\qquad(b)\;\large\frac{-1}{64}$$\qquad(c)\;\large\frac{1}{8}\qquad$$(d)\;\large\frac{-1}{8}$

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1 Answer

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$\sin\large\frac{9\pi}{14}$$\sin\large\frac{11\pi}{14}$$\sin\large\frac{13\pi}{14}$
$\Rightarrow \sin\large\frac{5\pi}{14}$$\sin\large\frac{3\pi}{14}$$\sin\large\frac{\pi}{14}$
$\Rightarrow \cos\large\frac{\pi}{7}$$\cos\large\frac{2\pi}{7}$$\cos\large\frac{3\pi}{7}$
$\Rightarrow -\cos\large\frac{\pi}{7}$$\cos\large\frac{2\pi}{7}$$\cos\large\frac{4\pi}{7}$
$\Rightarrow \large\frac{-\sin8\pi/7}{8\sin\pi/7}$
$\Rightarrow \large\frac{1}{8}$
Hence (c) is the right option.
answered Oct 8, 2013 by sreemathi.v
 

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