已知函数f(x)=2√3sin(x/2+π/4)cos(x/2+π/4)-sin(x+π)

来源：学生作业帮编辑：搜狗做题网作业帮分类：数学作业时间：2024/07/09 12:03:29

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

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
再问：不明白
再答： 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)

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