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Show that 16cos((2pi)/(15))cos((4pi)/(15...

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

Text Solution

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`16(cos.(2pi)/(15).cos.(4pi)/(15).cos.(8pi)/(15).cos.(16pi)/(15))`

`=16(cosA.cos 2Acos 2^(2)A. cos 2^(3) A) " "["Where, A" = (2pi)/(15)]`
`=16((sin2^(4)A)/(2^(4)sin A))=(sin2^(4)((2pi)/(15)))/(sin((2pi)/(15)))`
`=(sin((32pi)/(15)))/(sin((2pi)/(15)))=(sin(2pi+(2pi)/(15)))/(sin((2pi)/(15)))`
`=(sin((2pi)/(15)))/(sin((2pi)/(15)))=1`
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