三角函数求值问题已知函数f(x)=【sin(π/4+x)】【sin(π/4-x)】+√3sinxcosx,x∈R求f(π
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三角函数求值问题
已知函数f(x)=【sin(π/4+x)】【sin(π/4-x)】+√3sinxcosx,x∈R
求f(π/6)的值
在△ABC中,若f(A/2)=1,求sinB+sinC的最大值
已知函数f(x)=【sin(π/4+x)】【sin(π/4-x)】+√3sinxcosx,x∈R
求f(π/6)的值
在△ABC中,若f(A/2)=1,求sinB+sinC的最大值
f(x)=【sin(π/4+x)】【sin(π/4-x)】+√3sinxcosx
=v2/2(cosx+sinx)*v2/2(cosx-sinx)+v3sinxcosx
=1/2(cos^2x-sin^2x)+v3/2*2sinxcosx
=sinπ/6cos2x+cosπ/6sin2x
=sin(2x+π/6),
——》f(π/6)=sin(2π/6+π/6)=1;
f(A/2)=1,——》A=π/3,——》B=π-A-C=2π/3-C,
sinB+sinC
=sin(2π/3-C)+sinC
=v3/2cosC+1/2sinC+sinC
=v3(1/2cosC+v3/2sinC)
=v3sin(C+π/6)
=v2/2(cosx+sinx)*v2/2(cosx-sinx)+v3sinxcosx
=1/2(cos^2x-sin^2x)+v3/2*2sinxcosx
=sinπ/6cos2x+cosπ/6sin2x
=sin(2x+π/6),
——》f(π/6)=sin(2π/6+π/6)=1;
f(A/2)=1,——》A=π/3,——》B=π-A-C=2π/3-C,
sinB+sinC
=sin(2π/3-C)+sinC
=v3/2cosC+1/2sinC+sinC
=v3(1/2cosC+v3/2sinC)
=v3sin(C+π/6)
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