The numerical value of cos π/7+ cos 3π/7+cos 5π/7 is equal to
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Step-by-step explanation:
sin(2A) = 2sinAcosA
2sinAcosB = sin(A+B) + sin(A-B)
= 1/2sin(π/7) [ sin(2π/7) + sin(π/7+3π/7) + sin(π/7-3π/7) + sin(π/7+5π/7) + sin(π/7-5π/7) ]
= 1/2sin(π/7) [ sin(2π/7) + sin(4π/7) + sin(-2π/7) + sin(6π/7) + sin(-4π/7) ]
= 1/2sin(π/7) [ sin(2π/7) + sin(4π/7) - sin(2π/7) + sin(6π/7) - sin(4π/7) ]
= 1/2sin(π/7) [sin(6π/7)]
= 1/2sin(π/7) [sin(π - π/7)]
= [sin(π/7)]/2sin(π/7)
= ½
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