已知函数f(x)=2√3sin(x⼀2+π⼀4)cos(x⼀2+π⼀4)-sin(x+π)

f(x)=2√3(sinx/2cosπ/4+cosx/2sinπ/4)(cosx/2cosπ/4-sinx/2sinπ/4) - (sinxcosπ-cosxsinπ)

=2√3(√2/2sinx/2+√2/2cosx/2)(√2/2cosx/2-√2/2sinx/2)+sinπ
=2√3[1/2(cosx/2的平方－sinx/2的平方)+sinx
=√3[ (1+cosx)/2 - (1-cocx)/2 ]+sinx
=√3cosx+sinx
你可以写下来看

x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
f(x)=根号3sin[2(x/2+π/4)]+sinx
f(x)=根号3sin(x+π/2)+sinx

2sin(x/2+π/4)cos(x/2+π/4)=sin2(x/2+π/4)=sin(x+π/2)，用的是公式sin2x=2sinxcosx

sin(x+π/2)=cos[π/2-(x+π/2)]=cos(-x)=cosx，用的是公式sinx=cos(π/2-x)和cosx=cos(-x)

sin2x=2sinxcosx

sin(x+π)=-sinx

sin2x=2*Sinx*Cosx