sin65+sin15sin10
=cos25+sin15sin10
=cos(10+15)+sin15sin10(由和差化积公式)
=cos10cos15-sin10sin15+sin15sin10
=cos10cos15
类似地
sin25-cos15cos80
=sin25-cos15sin10
=sin(15+10)-cos15sin10 (由和差化积公式)
=sin15cos10+cos15sin10-cos15sin10
=sin15cos10
所以原式
(sin65+sin15sin10)/(sin25-cos15cos80)
=(cos10cos15)/(sin15sin10)
=cos15/sin15(分子分母同时乘以2cos15)
=2(cos15)^2/(2sin15cos15)(分子分母同时用倍角公式)
=(cos30+1)/sin30
=2+根号3
即原式=2+根号3.