Question

已知msinx+ncosx=a,ntanx-b／cosx=m求证m^2+n^2=a^2+b^2

Answer 1

ntanx-b／cosx=m ->nsinx-mcosx=ba^2=m^2sinx^2+n^2cos^2x+2mnsinxcosxb^2=n^2sin^2x+m^2cos^2x-2mnsinxcoxa^2+b^2=m^2sinx^2+n^2cos^2x+2mnsinxcosx+n^2sin^2x+m^2cos^2x-2mnsinxcox=m^2+n^2 得证