满足sin（x+sinx）=cos（x-cosx）的锐角x为几满足sin（x+sinx）=cos（x-cosx）的锐角x为几

满足sin（x+sinx）=cos（x-cosx）的锐角x为几满足sin（x+sinx）=cos（x-cosx）的锐角x为几
满足sin（x+sinx）=cos（x-cosx）的锐角x为几
满足sin（x+sinx）=cos（x-cosx）的锐角x为几

满足sin（x+sinx）=cos（x-cosx）的锐角x为几满足sin（x+sinx）=cos（x-cosx）的锐角x为几
cos(X-cosX)=sin(π/2-X+cosX)
带入原式
sin(x+sinx)=sin(π/2-x+cosx)
x+sinx=π/2-x+cosx
sinx-cosx=π/2-2x
对于原式左侧有
sinx-cosx
=√2(√2/2*sinx-√2/2cosx)
=√2(sinxcosπ/4-cosxsinπ/4)
=√2sin(x-π/4)
∴ √2sin(x-π/4)=π/2-2x
将x=π/4带入,易得原方程两侧都等于0
∴满足原方程的x∈(0,π/2)存在且x=π/4

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