Question

一道关于数学三角函数的题,哪位数学好的朋友帮哈忙,谢 证明sin(x+y)-sinx=2cos((2x+y)\2)sin

Answer 1

sin(x+y)-sinx=sinxcosy+cosysinx-sinx

2cos((2x+y)2)sin(y2)=2cos(x+y/2)sin(y/2)

=2[cosxcos(y/2)-sinxsin(y/2)]sin(y/2)

=2cosxcos(y/2)sin(y/2)-sinxsin(y/2)sin(y/2)

=sinycosx-sinx(1-cosy)

=sinycosx-sinx+sinxcosy

=sinxcosy+cosysinx-sinx

得证!