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Prove that: cos ((2pi)/15) . cos ((4pi)...

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

Text Solution

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`cos2pi/15*cos4pi/15*cos8pi/15*cos(pi+pi/15)`
`(2sinpi/15*cospi/15*cos2pi/15*cos4pi/15*cos8pi/15)/(2sinpi/15`
`(-2sin2pi/15cos2pi/15*cos4pi/15*cos8pi/15)/(2*2sinpi/15)`
`(-sin4pi/15cos4pi/15*cos8pi/15)/(24sinpi/15)`
`(sinpi/15)/(16sinpi/15)=1/16`
proved.
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