Question

已知实数a,b,c,d满足a²+b²=c²+d²=4,ac+bd=0,求ab+cd与ad-bc的值

Answer 1

问：已知实数a,b,c,d满足a²+b²=c²+d²=4,ac+bd=0,求ab+cd与ad-bc的值

答：ad-bc=±4

答：设a=sinx,b=cosx.c=siny,d=cosy.由ac+bd=0可得cosxcosy+sinxsiny=0即cos(x-y)=0∴x-y=90º∴x=90º+yab+cd=sinxcosx+sinycosy=sin(90+y)cos(90+y)+sinycosy=-sinycosy+sinycosy=0