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)=2sinx_数学解答

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,

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解答

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 =2s...