作业帮[2sin50+sin10(1+根号3*tan10)]*根号(2sin80*sin80)
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/06 20:37:01
![[2sin50+sin10(1+根号3*tan10)]*根号(2sin80*sin80)](/uploads/image/z/3177070-70-0.jpg?t=%5B2sin50%2Bsin10%281%2B%E6%A0%B9%E5%8F%B73%2Atan10%29%5D%2A%E6%A0%B9%E5%8F%B7%282sin80%2Asin80%29)
[2sin50+sin10(1+根号3*tan10)]*根号(2sin80*sin80)
[2sin50+sin10(1+根号3*tan10)]*根号(2sin80*sin80)
[2sin50+sin10(1+根号3*tan10)]*根号(2sin80*sin80)
sqrt(3)=tan60
1+sqrt(3)*tan10=1+tan60tan10=(sin60sin10+cos60cos10)/cos60cos10=cos50/cos60cos10=2cos50/cos10
sqrt(2sin80*sin80)=sqrt(2)sin80=sqrt(2)cos10
[2sin50+sin10(1+sqrt3*tan10)]*sqrt(2sin80*sin80)=[2sin50+2cos50sin10/cos10]sqrt(2)cos10=2sqrt(2)*(sin50cos10+cos50sin10)=2sqrt(2)*sin60=sqrt(6)