作业帮 > 数学 > 作业

数学三角函数 函数f(x)=2sinxcosx+2sin(x+π/4)sin(x+3π/4)+1.

来源:学生作业帮 编辑:拍题作业网作业帮 分类:数学作业 时间:2024/05/01 10:35:45
数学三角函数 函数f(x)=2sinxcosx+2sin(x+π/4)sin(x+3π/4)+1.
怎么把 函数f(x)=2sinxcosx+2sin(x+π/4)sin(x+3π/4)+1.拆开,再结合,
f(x)=2sinxcosx+2sin(x+π/4)sin(x+3π/4)+1
=2sinxcosx+2﹙sinxcosπ/4+cosxsinπ/4)﹙sinxcos3π/4+cosxsin3π/4)+1
=2sinxcosx+2﹙√2/2sinx+√2/2cosx)﹙√2/2cosx-√2/2sinx)+1
=2sinxcosx+2﹙1/2sinxcosx-1/2sin²x+1/2cos²x-1/2sinxcosx)+1
=2sinxcosx-sin²x+cos²x+1
=2sinxcosx-sin²x+cos²x+sin²x+cos²x
=2sinxcosx+2cos²x
=sin2x+coszx+1
=√2sin(2x+π/4﹚+1