函数f(x)=sin(-2x+π/3)+sin2x的最大值是

问题描述:

函数f(x)=sin(-2x+π/3)+sin2x的最大值是

f(x)=sin(π/3)cos(2x)-cos(π/3)sin(2x)+sin(2x)
=√3/2cos(2x)-1/2sin(2x)+sin(2x)
=√3/2cos(2x)+1/2sin(2x)
=sin(π/3)cos(2x)+cos(π/3)sin(2x)
=sin(2x+π/3)
最大值为1

f(x)=-sin(2x-π/3)+sin2x
=-1/2sin2x+√3/2cosx+sin2x
=1/2sin2x+√3/2cosx
=sin(2x+π/3)
故f(x)的最大值是1