Question

请教sin(a+b)-sina=2cos(a+b/2)sinb/2

Answer 1

这个是和差化积公式,

当然可以用两角和和差的正弦公式展开得到

sin(a+b)=sin(a+b/2+b/2)=sin(a+b/2)cos(b/2)+cos(a+b/2)sin(b/2)

sina=sin(a+b/2-b/2)=sin(a+b/2)cos(b/2)-cos(a+b/2)sin(b/2)

上面两式相减得到

sin(a+b)-sina=2cos(a+b/2)sin(b/2)