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

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)=1

A=π/3

sinB+sinC

=sin(2π/3-C)+sinC

=(√3/2)cosC-(1/2)sinC+sinC

=(√3/2)cosC+(1/2)sinC

=sin(C+π/3)

因为 0