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

Explanation

Here, we will use,

`2sinxcosx = sin2x`

Now,

`L.H.S. = 16cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)cos((16pi)/15)`

`=16cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)cos(pi+pi/15)`

`=16cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)(-cos(pi/15))`

`=-16cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)`

`=8/sin(pi/15)*2sin(pi/15)cos(pi/15)cos((2pi)/15)cos((4pi)/15)cos((8pi)/15)`

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