Question

Prove that `cos(2pi)/(15)cos(4pi)/(15)cos(8pi)/(15)cos(14pi)/(15)=1/(16)`

Answer 1

`cos2/15picos4/15picos8/15picos14/15pi=1/16`
`=-cospi/15cos2/15picos4/15picos8/15pi`
`=cosAcos2Acos2^2A....cosA^nA=(sin2^nA)/(2^nsinA)`
`A=pi/15`
`=-cosAcos2Aco2^2Acos2^3A`
`=(-sin2^4(16/15pi))/(2^4sin(pi/16))`
`=(-sin(16/15pi))/(16sin(pi/15))`
`=-[-sinpi/15]/(16sinpi/15)`
`cos2/15picos4/15picos8/15picos14/15pi=1/16`.