1.sin42-cos12+sin54=sin42-sin78+sin54
=sin54-sin18=2cos36sin18
=sin72/2cos18=1/2
2 cosA+cosB=2cos(A+B)/2*cos(A-B)/2 和差化积 不能这么化简：cos2π/7+cos6π/7=2cos4π/7*cos2π/7 cos2π/7+cos4π/7+cos6π/7=2cos4π/7*cos2π/7+cos4π/7=cos4π/7(1+2cos2π/7) 因为1+2cos2π/7,我们无法前进,我们要化成次数相等的齐次式：cos2π/7+cos4π/7+cos6π/7=2cos3π/7*cos1π/7+2[cos3π/7]-1=2cos3π/7(cos1π/7+cos3π/7)-1=4cos1π/7cos2π/7cos3π/7-1 4cos1π/7cos2π/7cos3π/7我们就有办法了 4cos1π/7cos2π/7cos3π/7=(sin1π/7*cos1π/7*cos2π/7*cos3π/7)/sin1π/7 用2sinA*cosA=sin2A 化(sin1π/7*cos1π/7*cos2π/7*cos3π/7)/sin1π/7=1/8 代入cos2π/7+cos4π/7+cos6π/7=4cos1π/7cos2π/7cos3π/7-1=-1/2