Question

已知函数f(x)=sin（x+π/6)+sin(x-π/6)+cosx+a的最大值为1.

Answer 1

f(x)=sinxcosπ/6+cosxsinπ/6+2sinxcosπ/6-cosxsinπ/6+cosx+a

=2sinxcosπ/6+cosx+a

=√3sinx+cosx+a

=2sin(x+π/6)+a

最大值=2+a=1

a=-1

f(x)=2sin(x+π/6)-1>=0

sin(x+π/6)>=1/2=sinπ/6=sin5π/6

所以2kπ+π/6