sinx+cosx+sinxcosx+1=√2*sin(x+π/4)+1/2 *sin2x+1是为什么?

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sinx+cosx+sinxcosx+1=√2*sin(x+π/4)+1/2*sin2x+1是为什么?sinx+cosx+sinxcosx+1=√2*sin(x+π/4)+1/2*sin2x+1是为什

sinx+cosx+sinxcosx+1=√2*sin(x+π/4)+1/2 *sin2x+1是为什么?
sinx+cosx+sinxcosx+1=√2*sin(x+π/4)+1/2 *sin2x+1是为什么?

sinx+cosx+sinxcosx+1=√2*sin(x+π/4)+1/2 *sin2x+1是为什么?
1.辅助角公式acosx+bsinx=√(a^2+b^2)sin(x+arctan(a/b))
2.二倍角公式
正弦二倍角公式:  sin2α = 2cosαsinα

  推导
  sin2α = sin(α+α) = sinαcosα + cosαsinα= 2sinαcosα

sinx+cosx提出前面的系数开根号=√2*sin(x+π/4)
而2sinxcosx=sin2x,所以sinxcosx=1/2 *sin2x
综上sinx+cosx+sinxcosx+1=√2*sin(x+π/4)+1/2 *sin2x+1