Question #a955b

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Question #a955b

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Answer 1 · 2017-02-07T00:48:53

$cos (\frac{180}{7}) cos (\frac{720}{7}) cos (\frac{900}{7})$ $cos(180/7) cos(720/7) cos(900 /7 )$
$= cos (\frac{π}{7}) cos (\frac{4 π}{7}) cos (\frac{5 π}{7})$ $=cos(pi/7) cos((4pi)/7) cos((5pi) /7 )$

$= cos (\frac{π}{7}) cos (\frac{5 π}{7}) cos (\frac{4 π}{7})$ $=cos(pi/7) cos((5pi)/7) cos((4pi) /7 )$

$= cos (\frac{π}{7}) cos (π - \frac{2 π}{7}) cos (\frac{4 π}{7})$ $=cos(pi/7) cos(pi-(2pi)/7) cos((4pi) /7 )$

$= - \frac{8 sin (\frac{π}{7}) cos (\frac{π}{7}) cos (\frac{2 π}{7}) cos (\frac{4 π}{7})}{8 sin (\frac{π}{7})}$ $=-(8sin(pi/7)cos(pi/7) cos((2pi)/7)cos((4pi) /7 ))/(8sin(pi/7))$

$= - \frac{4 sin (\frac{2 π}{7}) cos (\frac{2 π}{7}) cos (\frac{4 π}{7})}{8 sin (\frac{π}{7})}$ $=-(4sin((2pi)/7)cos((2pi)/7)cos((4pi) /7 ))/(8sin(pi/7))$

$= - \frac{2 sin (\frac{4 π}{7}) cos (\frac{4 π}{7})}{8 sin (\frac{π}{7})}$ $=-(2sin((4pi)/7)cos((4pi) /7 ))/(8sin(pi/7))$

$= - \frac{sin (\frac{8 π}{7})}{8 sin (\frac{π}{7})}$ $=-(sin((8pi)/7))/(8sin(pi/7))$

$= - \frac{sin (π + \frac{π}{7})}{8 sin (\frac{π}{7})}$ $=-(sin(pi+pi/7))/(8sin(pi/7))$

$= \frac{sin (\frac{π}{7})}{8 sin (\frac{π}{7})}$ $=(sin(pi/7))/(8sin(pi/7))$

$= \frac{1}{8}$ $=1/8$

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Question #a955b

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