（sin65+sin15sin10) / (sin25-cos15cos80)求值?

原式=(cos25+sin15sin10)/(sin25-cos15sin10)
=[cos(15+10)+sin15sin10)/[sin(15+10)-sin10cos15]
=(cos15cos10-sin15sin10+sin15sin10)/(sin15cos10+cos15sin10-sin15cos10)
=cos15cos10/cos15sin10
=cos10/sin10
=cot10

(sin65+sin15sin10)/(sin25-cos15cos80)
=[sin(90-25)+sin15sin10]/[sin(15+10)-cos15cos(90-10)]
=(cos25+sin15sin10)/(sin15cos10＋cos15sin10-cos15sin10)
=[cos(15+10)+sin15sin10]/sin15cos10
=(cos15cos10-sin15sin10+sin15sin10)/sin15cos10
=cos15/sin15
=cot15
=tan75
=2+根号3

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.