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
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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(y\2)
有点急,喜欢数学的朋友来帮哈忙哈,
对不起,我再查查
有点急,喜欢数学的朋友来帮哈忙哈,
对不起,我再查查
sin(x+y)-sinx=sinxcosy+cosysinx-sinx
2cos((2x+y)\2)sin(y\2)=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!
2cos((2x+y)\2)sin(y\2)=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!
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