Prove that cos 2pi/15 cos4pi/15 cos 8pi/15 cos14pi/15=1/16.share all relevant formulae and give a detailed explanation pls.

cos(2π/15) cos(4π/15) cos(8π/15) cos(14π/15) 
= cos(2π/15) cos(4π/15) cos(8π/15) cos(π – (π/15)) 
= cos(2π/15) cos(4π/15) cos(8π/15) * -cos(π/15) 
= -cos(π/15) cos(2π/15) cos(4π/15) cos(8π/15) 
= -16sin(π/15) cos(π/15) cos(2π/15) cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ] 
= -8 * [ 2sin(π/15) cos(π/15) ] cos(2π/15) cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ] 
= -8 sin(2π/15) cos(2π/15) cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ] 
= -4 * [ 2 sin(2π/15) cos(2π/15) ] cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ] 
= -4 sin(4π/15) cos(4π/15) cos(8π/15) / [ 16 sin(π/15) ] 
= -2 * [2 sin(4π/15) cos(4π/15) ] cos(8π/15) / [ 16 sin(π/15) ] 
= -2 sin(8π/15) cos(8π/15) / [ 16 sin(π/15) ] 
= -sin(16π/15) / [ 16 sin(π/15) ] 
= -sin(π + π/15) / [ 16 sin(π/15) ] 
= -1 * -sin(π/15) / [ 16 sin(π/15) ] 
= 1/16

c

step-by-step explanation: