高中数学——三角恒等变换
来源:学生作业帮 编辑:搜狗做题网作业帮 分类:数学作业 时间:2024/08/05 07:21:29
高中数学——三角恒等变换
计算:
(sin115°+sin15°sin10°)/(sin155°-cos15°cos80°)=?
计算:
(sin115°+sin15°sin10°)/(sin155°-cos15°cos80°)=?
![高中数学——三角恒等变换](/uploads/image/z/19213211-11-1.jpg?t=%E9%AB%98%E4%B8%AD%E6%95%B0%E5%AD%A6%E2%80%94%E2%80%94%E4%B8%89%E8%A7%92%E6%81%92%E7%AD%89%E5%8F%98%E6%8D%A2)
(sin115+sin15sin10)/(sin155-cos15cos80)
=(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)/(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