为什么sin(x+h)-sinx=2cos(x+h/2)sin(h/2)
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sin(x+h)-sinx=sinxcosh+sinhcosx-sinx
=sinx(1-2sin²h/2)+2sin(h/2)cos(h/2)cosx-sinx
=-2sinxsin²(h/2)+2sin(h/2)cos(h/2)cosx
=2sin(h/2)[cos(h/2)cosx-sin(h/2)sinx)
=2cos(x+h/2)sin(h/2)
=sinx(1-2sin²h/2)+2sin(h/2)cos(h/2)cosx-sinx
=-2sinxsin²(h/2)+2sin(h/2)cos(h/2)cosx
=2sin(h/2)[cos(h/2)cosx-sin(h/2)sinx)
=2cos(x+h/2)sin(h/2)
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