Question

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

Answer 1

`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`