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Question Number 21009 by xxyy@gmail.com last updated on 10/Sep/17

Answered by Tinkutara last updated on 10/Sep/17

$${2\cos }^2\frac{\pi }{16}\times {2\cos }^2\frac{3\pi }{16}\times {2\cos }^2\frac{5\pi }{16}\times {2\cos }^2\frac{7\pi }{16}$$$$={\left(4\cos \frac{\pi }{16}\cos \frac{3\pi }{16}\cos \frac{5\pi }{16}\cos \frac{7\pi }{16}\right)}^2$$$$={\left(4\cos \frac{\pi }{16}\cos \frac{3\pi }{16}\sin \frac{3\pi }{16}\sin \frac{\pi }{16}\right)}^2$$$$={\left(\sin \frac{\pi }{8}\sin \frac{3\pi }{8}\right)}^2=\frac{1}{4}{\left(2\sin \frac{\pi }{8}\cos \frac{\pi }{8}\right)}^2$$$$=\frac{1}{4}{\sin }^2\frac{\pi }{4}=\frac{1}{8}$$

Commented by xxyy@gmail.com last updated on 10/Sep/17

$$\mathrm{thank}\mathrm{very}\mathrm{much}\mathrm{sir}!$$

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