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$\cos 2^3\large\frac{\pi}{10}$$\cos 2^4\large\frac{\pi}{10}$$\cos 2^5\large\frac{\pi}{10}........$$\cos 2^{10}\large\frac{\pi}{10}$ is equal to

$(a)\;\large\frac{1}{128}$$\qquad(b)\;\large\frac{1}{256}$$\qquad(c)\;\large\frac{1}{512}$$\sin\large\frac{\pi}{10}$$\qquad(d)\;\large\frac{\sqrt 5-1}{512}$$\sin\large\frac{3\pi}{10}$

1 Answer

$\cos 2^3\large\frac{\pi}{10}$$\cos 2^4\large\frac{\pi}{10}$$\cos 2^5\large\frac{\pi}{10}........$$\cos 2^{10}\large\frac{\pi}{10}$
$\Rightarrow \large\frac{\sin 2^{11}\Large\frac{\pi}{10}}{256\sin 2^3\Large\frac{\pi}{10}}$
$\Rightarrow \large\frac{1}{256}$
Hence (b) is the correct answer.
answered Oct 8, 2013 by sreemathi.v
 
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