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∈(
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![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∈(](/uploads/image/z/8930458-10-8.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%5D2.%E5%B7%B2%E7%9F%A5+%CF%80%2F2%EF%BC%9C%CE%B2%EF%BC%9C%CE%B1%EF%BC%9C3%CF%80%2F4%2Csin%EF%BC%88%CE%B1%2B%CE%B2%EF%BC%89%3D-3%2F5%2Ccos%EF%BC%88%CE%B1-%CE%B2%29%3D12%2F13%2C%E6%B1%82cos2%CE%B1%E7%9A%84%E5%80%BC.3.%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%28t%29%3D%281-t%2F1%2Bt%29%E5%BC%80%E6%A0%B9%2Cg%28x%29%3Dcosx%C2%B7f%28sinx%29%2Bsinx%C2%B7f%28cosx%29%2C%E5%85%B6%E4%B8%ADx%E2%88%88%EF%BC%88)
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∈(
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.
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∈(
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
1、原式=[cos40°+sin50°(1+√3*sin10°/cos10°)]/(√2*(cos20)^2)
=[cos40°+2(sin50°/cos10°)*(1/2cos10°+√3/2sin10°)]/
√2*(cos20)^2)
=[cos40°+2(sin50°/cos10°)*(sin40°)]/√2*(cos20)^2)
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1、原式=[cos40°+sin50°(1+√3*sin10°/cos10°)]/(√2*(cos20)^2)
=[cos40°+2(sin50°/cos10°)*(1/2cos10°+√3/2sin10°)]/
√2*(cos20)^2)
=[cos40°+2(sin50°/cos10°)*(sin40°)]/√2*(cos20)^2)
=[cos40°+sin80°/cos10°]/(√2*(cos20)^2)
=[cos40°+1]/(√2*(1+cos40°)/2)
=√2
2、讲讲思路吧!cos2α=cos[(α+β)+(α-β)]
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1) 1+ 根3 ×tan10°=(cos10+根3*sin10)/cos10
=2*(1/2*cos10+1/(根3)*sin10)/cos10=2*sin40/cos10
=2*sin40/sin80=1/cos40=1/sin50
cos40°+sin50°(1+ 根3 ×tan10°)=1+cos40
sin70°×根(1+cos40°)=sin70*根2...
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1) 1+ 根3 ×tan10°=(cos10+根3*sin10)/cos10
=2*(1/2*cos10+1/(根3)*sin10)/cos10=2*sin40/cos10
=2*sin40/sin80=1/cos40=1/sin50
cos40°+sin50°(1+ 根3 ×tan10°)=1+cos40
sin70°×根(1+cos40°)=sin70*根2*cos20=根2*(sin70)^2
=根2/2*(1-cos140)=根2/2*(1+cos40)
[cos40°+sin50°(1+ 根3 ×tan10°)]÷[sin70°×根(1+cos40°)]=根2
2、π<α+β<3π/2,0<α-β<π/4
coc(α+β)=-4/5,sin(α-β)=5/13
cos2α=cos[(α+β)+(α-β)]=coc(α+β)*cos(α-β)-sin(α+β)*sin(α-β)=33/65
3、f(sinx)=(sin(x/2)-cos(x/2))/(sin(x/2)+cos(x/2))
f(cosx)=sin(x/2)/cos(x/2)
g(x)=-(sin(x/2)-cos(x/2))^2+2*(sin(x/2))^2=sinx-cosx=根2*sin(x+7π/4)
[-根2/2,1/2)
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1、[cos40°+sin50°*2(cos10°sin30°/cos10°+ cos30° ×tan10)]÷[sin70°×根(2cos20°^2)]
=[cos40°+sin50°*2*(sin40°/cos10°)]÷[sin70°×cos20°根(2)]
=[cos40°+cos40°*2*(sin40°/cos10°)]÷[sin70°×cos20°根(2)]
...
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1、[cos40°+sin50°*2(cos10°sin30°/cos10°+ cos30° ×tan10)]÷[sin70°×根(2cos20°^2)]
=[cos40°+sin50°*2*(sin40°/cos10°)]÷[sin70°×cos20°根(2)]
=[cos40°+cos40°*2*(sin40°/cos10°)]÷[sin70°×cos20°根(2)]
=[cos40°+(sin80°/cos10°)]÷[sin70°×cos20°根(2)]
=[cos40°+1]÷[cos20°×cos20°根(2)]
=(2COS20^2)]÷[cos20°×cos20°
=根(2)
2、π/2<β<α<3π/4 π<α+β<3π/2 sin(α+β)=-3/5 cos(α+β)=-4/5
0<α-β<π/2cos(α-β)=12/13 sin(α-β)=5/13
cos2α=cos(α+β+α-β)=cos(α+β)cos(α-β)-sin(α+β)sin(α-β)=-33/65
3、f(t)=(1-t/1+t)开根 x∈(π , 17π/12]. cosx<0
sinx<0
f(sinx)=(1-sinx/1+sinx)开根=(分子分母同时乘1-sinx)=sinx-1/cosx
f(cosx)=(1-cosx/1+cosx)开根=分子分母同时乘1-cosx=1-cosx/-sinx
g(x)=cosx·f(sinx)+sinx·f(cosx)=sinx-1-1+cosx=sinx+cosx-2=根2*sin(X+ ψ)-2
sinψ=根2/2 cosψ=根2/2 ψ=π/4 A=根2 ω=1
(2)x∈(π , 17π/12].x+ψ∈(5π/4 , 5π/3].
在x+ψ=5π/3取最大 x+ψ= 3π/2取最小
max=2-根3 /2 min=-3
g(x) 值域是闭区间【-3,2-根3/2】
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