1.化简:[cos40°+sin50°(1+ 根3 ×tan10°)]÷[sin70°×根(1+cos40°)]
来源:学生作业帮 编辑:百度作业网作业帮 分类:数学作业 时间:2024/08/17 07:09:33
1.化简:[cos40°+sin50°(1+ 根3 ×tan10°)]÷[sin70°×根(1+cos40°)]
2.已知 π/2<β<α<3π/4,sin(α+β)=-3/5,cos(α-β)=12/13,求cos2α的值.
3.已知函数f(t)=(1-t/1+t)开根,g(x)=cosx·f(sinx)+sinx·f(cosx),其中x∈(π ,17π/12].
⑴将函数g(x)化简成Asinx(ωx+ψ)+B的形式,(A>0 ω>0 ψ∈[0 ,2π)
⑵求函数g(x)的值域.
2.已知 π/2<β<α<3π/4,sin(α+β)=-3/5,cos(α-β)=12/13,求cos2α的值.
3.已知函数f(t)=(1-t/1+t)开根,g(x)=cosx·f(sinx)+sinx·f(cosx),其中x∈(π ,17π/12].
⑴将函数g(x)化简成Asinx(ωx+ψ)+B的形式,(A>0 ω>0 ψ∈[0 ,2π)
⑵求函数g(x)的值域.
![1.化简:[cos40°+sin50°(1+ 根3 ×tan10°)]÷[sin70°×根(1+cos40°)]](/uploads/image/z/16354924-52-4.jpg?t=1.%E5%8C%96%E7%AE%80%EF%BC%9A%5Bcos40%C2%B0%2Bsin50%C2%B0%EF%BC%881%2B+%E6%A0%B93+%C3%97tan10%C2%B0%EF%BC%89%5D%C3%B7%5Bsin70%C2%B0%C3%97%E6%A0%B9%EF%BC%881%2Bcos40%C2%B0%EF%BC%89%5D)
sin70=cos20 sin50=cos40
cos10+√3sin10
=2(1/2cos10+√3/2sin10)
=2(sin30cos30+sin10+cos30)
=2sin40
cos10=sin80=2cos40sin40
(cos20)^2=(1+cos40)/2
[cos40+sin50(1+√3*tan10)]/[sin70*√(1+cos40)]
=[sin50+cos40(1+√3sin10/cos10)]/(cos20)^2 (分子分母同*cos10 )
=[sin50cos10+cos40(cos10+√3sin10)]/(cos20)^2cos10
=[sin50cos10+2cos40sin40]/(cos20)^2cos10
=[sin50cos10+cos10]/(cos20)^2cos10
=[cos40+1]/(cos20)^2
=2
2.
π/2
cos10+√3sin10
=2(1/2cos10+√3/2sin10)
=2(sin30cos30+sin10+cos30)
=2sin40
cos10=sin80=2cos40sin40
(cos20)^2=(1+cos40)/2
[cos40+sin50(1+√3*tan10)]/[sin70*√(1+cos40)]
=[sin50+cos40(1+√3sin10/cos10)]/(cos20)^2 (分子分母同*cos10 )
=[sin50cos10+cos40(cos10+√3sin10)]/(cos20)^2cos10
=[sin50cos10+2cos40sin40]/(cos20)^2cos10
=[sin50cos10+cos10]/(cos20)^2cos10
=[cos40+1]/(cos20)^2
=2
2.
π/2
『cos40°+sin50°(1+√3tan10°)』/sin70°√1+cos40°』
[cos40°+sin50°(1+√3tan10°)]/[sin70°√(1+cos40°)]=
(cos40°+sin50°(1+√3tan10°))/sin70°√(1+cos40°)
[cos40°+sin50°(1+√3tan10°)]/[sin70°√(1+cos40°)]=?
求值:cos40°+sin50°(1+3tan10°)sin70°1+sin50°
化简:(cos40+sin50(1+√3tan10))/(sin70√(1+cos40))
求值{cos40°+sin50°(1+根号3tan10°)}/1+sin50°
化简{sin50°+cos40°(1+根号3*tan10°)}/sin平方70°,详细步骤
化简:[sin50°+cos40°(1+根号3tan10°)]/sin²70°
化简sin50°+cos40°(1+√3tan10°)/sin^270°
coos40+sin50(1+(根号3)tan10)/sin70根号(1+cos40)
求值:cos40°(1+3tan10°)