COSπ/15-COS2π/15-COS4π/15+COS7π/15= 2009年江西数学预赛的题 要详解

原式=(cos7π/15+cosπ/15)-(cos4π/15+cos2π/15)
=2cos4π/15cosπ/5-2cosπ/5cosπ/15
=2cosπ/5(cos4π/15-cosπ/15)
=-4cosπ/5sinπ/6sinπ/10
=-2cosπ/5cos2π/5
=(-2sinπ/5cosπ/5cos2π/5)/(sinπ/5)
=-(sin2π/5cos2π/5)/(sinπ/5)
=-(sin4π/5)(2sinπ/5)=-1/2