作业帮[2sin50+sin10(1+根号3tan10)]sin80
来源：学生作业帮助网 编辑：作业帮 时间：2024/06/04 13:41:06
![[2sin50+sin10(1+根号3tan10)]sin80](/uploads/image/z/1344653-53-3.jpg?t=%5B2sin50%2Bsin10%281%2B%E6%A0%B9%E5%8F%B73tan10%29%5Dsin80)
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[2sin50+sin10(1+根号3tan10)]sin80
[2sin50+sin10(1+根号3tan10)]sin80
[2sin50+sin10(1+根号3tan10)]sin80
那是"根号3tan10"还是"根号3"
我就当是根号3了 sin后的2是平方
原式=[2sin(60-10)+sin10+(√3)sin2(10)/cos10]sin(90-10) 用公式sin(A-B)=sinAcosB-cosAsinB
=[(√3)cos10-sin10+sin10+(√3)sin2(10)/cos10 ]cos10
=(√3)cos2(10)+(√3)sin2(10)
=(√3)[cos2(10)+sin2(10)] sin2A+cos2B=1
=√3
[2sin50+sin10(1+根号3tan10)]sin80 (sin80=cos10)
=2sin50cos10+sin10(cos10+√3*sin10)
=2sin50cos10+sin10*2(1/2*cos10+√3/2*sin10)
=2sin50cos10+2sin10sin(10+30)
=2sin50cos10+2sin10cos50 (sin40=cos50)
=2sin(50+10)
=2sin60
=√3