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Question

Find :cosπ65cos2π65cos4π65cos8π65cos16π65cos32π65.

A
164
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B
132
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C
116
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D
None of these
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Solution

The correct option is A 164
Multiply by 12sin(π/65)×2sin(π65)
12sin(π/65)×2sin(π65)[cosπ65cos2π65cos4π65cos8π65cos16π65cos32π65]
sin2θ=2sinθcosθ
122sin(π/65)×2sin2π65×cos2π65×cos4π65×cos8π65×cos16π65×cos32π65
12×22sin(2π/65)×2sin4π65×cos4π65×cos8π65×cos16π65×cos32π65
12×23sin(2π/65)×2sin8π65cos8π65cos16π65cos32π65
126×sin(π/65)×sin(6ππ65)=164sin(π/65)×sin(ππ/65)
sinθ=sin(πθ)
164sin(π/65)×sin(π/65)=164
Hence proved

1061674_1037177_ans_88ecd767e0d24fe1bb4de5d8b4cdebea.png

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