请问sin(x+h)-sin x如何转换成2cos(x+h/2)sin h/2
问题描述：
请问sin(x+h)-sin x如何转换成2cos(x+h/2)sin h/2
中间我不知道通过哪些步骤,希望各位指教.
答
sin(x+h)-sinx = sinxcosh+cosxsinh-sinx = sinx(cosh-1)+cosxsinh = 2cosxsin(h/2)cos(h/2)-2sinxsin^2(h/2) = 2sin(h/2){cosxcos(h/2)-sinxsin(h/2)} = 2sin(h/2)cos(x+h/2) = 2cos(x+h/2)sinh/2