作业帮求[2sin50+sin10(1+√3*tan10)]sin80的值.
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/01 09:49:16
![求[2sin50+sin10(1+√3*tan10)]sin80的值.](/uploads/image/z/8586109-37-9.jpg?t=%E6%B1%82%5B2sin50%2Bsin10%281%2B%E2%88%9A3%2Atan10%29%5Dsin80%E7%9A%84%E5%80%BC.)
求[2sin50+sin10(1+√3*tan10)]sin80的值.
求[2sin50+sin10(1+√3*tan10)]sin80的值.
求[2sin50+sin10(1+√3*tan10)]sin80的值.
[2sin50+sin10(1+√3*tan10)]sin80
=[2sin50+sin10+√3 *sin10*sin10/cos10]cos10
=2sin50cos10+sin10cos10+√3 *sin10*sin10
=2sin50cos10+2sin10(1/2cos10++√3/2 *sin10)
=2sin50cos10+2sin10sin(30+10)
=2sin50cos10+2sin10sin40
=2(sin50cos10+cos50sin10)
=2sin(50+10)
2sin60
=√3
原式=[2sin50+sin10*（(2sin10sin40)/cos10)]cos10 通分
=(2cos40cos10+2sin10sin40)/cos10*cos10
=2cos40