Question

已知函数f(x)=sinx/2cosx/2+根号3cos平方x/2求当x∈【0,π】时,f(x)的零点

Answer 1

f(x)=sinx/2cosx/2+根号3cos平方x/2

=(1/2)sinx+√3/2(1+cosx)

=(1/2)sinx+(√3/2)cosx+√3/2

=sinxcos(π/3)+cosxsin(π/3)+√3/2

=sin(x+π/3)+√3/2=0

sin(x+π/3)= -√3/2

x∈【0,π】,x+π/3∈【π/3,4π/3】

所以 x+π/3=4π/3

x=π

当x∈【0,π】时,f(x)的零点为π