[2sin50+sin10(1+根号3*tan10)]*根号(2sin80*sin80)
来源:学生作业帮 编辑:神马作文网作业帮 分类:数学作业 时间:2024/09/23 00:38:20
[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)
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)
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