Question

已知函数f(x)=sin(x+6分之π)+sin(x-6分之π)+cosx+a(a属于R,a是常数).(1)求函数f(x

Answer 1

f(x)=sin(x+π/6)+sin(x-π/6)+cosx+a

=sinx*cos(π/6)+cosx*sin(π/6)+sinx*cos(π/6)-cosx*sin(π/6)+cosx+a

=（√3）sinx+cosx+a

=2sin(x+π/3)+a

所以T=2π/1=2π

注：a*sin(x)+b*cos(x)=(√a^2+b^2)sin(x+y)

(tan(y)=a/b)