Question #a955b

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Answer 1 · 2017-02-07T00:48:53

$cos(180/7) cos(720/7) cos(900 /7 )$
$=cos(pi/7) cos((4pi)/7) cos((5pi) /7 )$

$=cos(pi/7) cos((5pi)/7) cos((4pi) /7 )$

$=cos(pi/7) cos(pi-(2pi)/7) cos((4pi) /7 )$

$=-(8sin(pi/7)cos(pi/7) cos((2pi)/7)cos((4pi) /7 ))/(8sin(pi/7))$

$=-(4sin((2pi)/7)cos((2pi)/7)cos((4pi) /7 ))/(8sin(pi/7))$

$=-(2sin((4pi)/7)cos((4pi) /7 ))/(8sin(pi/7))$

$=-(sin((8pi)/7))/(8sin(pi/7))$

$=-(sin(pi+pi/7))/(8sin(pi/7))$

$=(sin(pi/7))/(8sin(pi/7))$

$=1/8$