求证cosπ/5 + cos3π/5=1/2

问题描述:

求证cosπ/5 + cos3π/5=1/2

cos36+cos108=cos(72-36)+cos(72+36)=cos72*cos36+sin72*sin36+cos72*cos36-sin72*sin36=2cos72*cos36=2sin18*cos36=sin36*cos36/cos18=sin72/2*cos18=cos18/2*cos18=1/2