已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
问题描述：
已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
=√3sin(x+π/2)+sinx
这一步是怎么来的
答
x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)
f(x)=根号3sin[2(x/2+π/4)]+sinx
f(x)=根号3sin(x+π/2)+sinx不明白sin(2x)=2sinxcosx这是公式所以：2√3sin(x/2+π/4)cos(x/2+π/4)=根号3sin[2(x/2+π/4)]sin(x+π)=-sinx 也是公式-sin(x+π)=-（-sinx)=sinx=√3sin(x+π/2)+sinx=-根号3cosx+sinx=2(-根号3/2cosx+1/2sinx)=2(cos5π/6cosx+sin5π/6sinx)=2cos(x-5π/6)