已知函数f(x)=sin(π/4+x)sin(π/4-x)+√3sinxcosx,我化简的sin(π/6+2x),让求在三角形ABC,若f(A/2)=1求sinB+sinC的最大值

Question

已知函数f(x)=sin(π/4+x)sin(π/4-x)+√3sinxcosx,我化简的sin(π/6+2x),让求在三角形ABC,若f(A/2)=1 求sinB+sinC的最大值

Answer 1

f(x)=sin(π/4+x)sin(π/4-x)+√3sinxcosx=sin(π/4+x)cos(x+π/4)+√3sinxcosx=(1/2)sin(π/2+2x)+√3sinxcosx =(1/2)cos2x+√3/2sin2x=sin(2x+π/6)f(A/2)=sin(A+π/6)=1A=π/3sinB+sinC=sin(2π/3-C)+sinC=(√3/2...