sin(x+t)-sinx=2cos(x+t/2)sint/2 如何证明?

sin(x+t)-sinx=2cos(x+t/2)sint/2 如何证明?
sin(x+t)-sinx=2cos(x+t/2)sint/2 如何证明?

sin(x+t)-sinx=2cos(x+t/2)sint/2 如何证明?
证明：
sin(x+t)-sinx
=sinxcost+cosxsint-sinx
=sinx(cost-1)+cosxsint
=-2sinx(sint/2)^2+2cosxcost/2sint/2
=2sint/2(-sinxsint/2+cosxcost/2)
=2sint/2cos(x+t/2)