How do you evaluate $Cos(pi/7)cos((4pi)/7)cos((5pi)/7)$ ?

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Answer 1 · 2016-10-03T15:37:44

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

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

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

$=-1/(8sin(pi/7))xx(2sin((4pi)/7)cos((4pi)/7))$

$=-1/(8sin(pi/7))sin((8pi)/7)$

$=-1/(8sin(pi/7))sin(pi+pi/7)$

$=-1/(8sin(pi/7))(-sin(pi/7))$

$=1/8$

How do you evaluate Cos(pi/7)*cos((4*pi)/7)*cos((5*pi)/7)Cos(pi/7)*cos((4*pi)/7)*cos((5*pi)/7)?