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The value of sinpi/(14)sin(3pi)/(14)sin(...

The value of `sinpi/(14)sin(3pi)/(14)sin(5pi)/(14)sin(7pi)/(14)sin(9pi)/(14)sin(11pi)/(14)sin(13pi)/(14)` is equal to___________

Text Solution

Verified by Experts

The correct Answer is:
`1//8`
`sin""(9pi)/(14)sin""(11pi)/(14)sin""(13pi)/(14)`
`=sin""(5pi)/(14)sin""(3pi)/(14)sin""(pi)/(14)`
`=cos""(pi)/(8)cos""(2pi)/(7)cos""(3pi)/(7)`
`=-cos""(pi)/(7)cos""(2pi)/(7)cos ""(4pi)/(7)`
`-(sin""(8pi)/(7))/(8sin""(pi)/(7))=(1)/(8)`
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