求证第6题2问,请大神把证明写在纸上拍过来,

Question

求证第6题2问,请大神把证明写在纸上拍过来,
 

Answer 1

[sin(x+2h)-sinx]/(2h)={sin[(x+h)+h]-sin[(x+h)-h]}/(2h)
=[sin(x+h)cosh+cos(x+h)sinh-sin(x+h)cosh+cos(x+h)sinh]/(2h)
=2cos(x+h)sinh/(2h)
=cos(x+h)sinh/h.
相当于用了和差化积公式.