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Question Number 119109 by bagjagunawan last updated on 22/Oct/20
Answered by 1549442205PVT last updated on 22/Oct/20
P=(12+cosπ20)(12+cos3π20)(12+cos9π20)(12+cos27π20)=(12+cos9)(12+cos81)(12+cos27)(12−cos63)=(14+cos9+cos812+cos9cos81)×(14+cos27−cos632−cos27cos63)=(14+cos45cos36+cos90+cos722)×(14+sin18sin45−cos90+cos362)=(14+22cos36+sin182)(14+22sin18−cos362)(1)∙sin36=cos54⇔2sin18cos18=4cos318−3cos18⇔2sin18=4cos218−3=4(1−sin218)−3⇒4sin218+2sin18−1=0sin18=5−14⇒cos36=1−2sin218=1−3−54=5+14.Replaceinto(1)wegetP=(14+22.5+14+5−18)×(14+22.5−14−5+18)=5+1+2(5+1)8×2(5−1)−5+18=10+1+5+28.10+1−(5+2)8=11+210−(7+210)64=116
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