解一个数学三角涵数题

sinαsinβ=-1/2[cos(α+β)-cos(α-β)]
cosαcosβ=1/2[cos(α+β)+cos(α-β)]
sinαcosβ=1/2[sin(α+β)+sin(α-β)]
cosαsinβ=1/2[sin(α+β)-sin(α-β)]
高中数学选记的公式“积化和差”
最好记住很有帮助
那么原式=1/2[sin(12°+18°)+sin(12°-18°)]+1/2[sin(78°+72°)+sin(78°-72°)]
=1/2[sin30°+sin(-6°)]+1/2[sin150°+sin6°]
=1/2（1/2-sin6°+1/2+sin6°）
=1/2

其中sin30°=sin150°=1/2
sin(-6°)=-sin6°

78+12=90;72+18=90
sin78°=cos12°
cos72°=sin18°
sin12°cos18°+sin78°cos72° =sin12°cos18°+cos12°sin18°
=sin(12°+18°)
=sin30°=1/2

sin12°cos18°+sin78°cos72°=sin12°cos18°+cos12°sin18°
=sin(12+18)°=sin30°=1/2

sin12°cos18°+sin78°cos72°=sin12°sin72°+cos12°cos72°=cos(12°-72°)=cos(-60°)=1/2=0.5

解：
sin12° cos18° +sin78° cos72°
=sin12° sin72° +cos12° cos72°
=cos(72° -12° )
=cos60°
=1/2