作业帮求值:[sin50°(1+tan10°√3)-cos20°]/[cos80°乘以根号下1-cos20°]
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 18:24:16
![求值:[sin50°(1+tan10°√3)-cos20°]/[cos80°乘以根号下1-cos20°]](/uploads/image/z/675142-70-2.jpg?t=%E6%B1%82%E5%80%BC%3A%5Bsin50%C2%B0%281%2Btan10%C2%B0%E2%88%9A3%29-cos20%C2%B0%5D%2F%5Bcos80%C2%B0%E4%B9%98%E4%BB%A5%E6%A0%B9%E5%8F%B7%E4%B8%8B1-cos20%C2%B0%5D)
求值:[sin50°(1+tan10°√3)-cos20°]/[cos80°乘以根号下1-cos20°]
求值:[sin50°(1+tan10°√3)-cos20°]/[cos80°乘以根号下1-cos20°]
求值:[sin50°(1+tan10°√3)-cos20°]/[cos80°乘以根号下1-cos20°]
（sin50°(1+√3*tan10°)-cos20°）/（cos80°*√（1-cos20°）)
=（sin50°(1+√3*sin10°/cos10°)-cos20°）/（cos80°*√（1-cos20°））
=(sin50°((cos10°+√3*sin10°)/cos10°)-cos20°）/（cos80°*√(2(sin10°)^2))
=(sin50°((1/2)cos10°+(√3/2)*sin10°)/((1/2)*cos10°)-cos20°）/（cos80°*√(2(sin10°)^2))
=(sin50°(sin30°*cos10°+cos30°*sin10°)/(1/2)*cos10°-cos20°）/（(√2)cos80°*sin10°)
=(sin50°*sin40°/(1/2)*cos10°-cos20°）/（(√2)sin10°*sin10°)
=(sin50°*cos50°/(1/2)*cos10°-cos20°）/（(√2)sin10°*sin10°)
=((1/2)sin100°/(1/2)*cos10°-cos20°）/（(√2)sin10°*sin10°)
=((1/2)sin80°/(1/2)*cos10°-cos20°）/（(√2)sin10°*sin10°)
=((1/2)cos10/(1/2)*cos10°-cos20°）/（(√2)sin10°sin10°)
=(1-cos20°)/（(√2)sin10°sin10°)
=2(sin20°)^2/(√2)(sin20°)^2
=2/√2
=√2