Question

已知sinx=1/3,sin(x+y)=1,则sin（2y+x)=

Answer 1

一般这里的x，y都属于锐角

sin(x+y)=1
sin(2x+2y)=0 cos(2x+2y)=-1

sin(2y+x)=sin[(2x+2y)-x]
=sin(2x+2y)cosx-sinxcos(2x+2y)
=0-1/3*(-1)
=1/3

Answer 2

sin(x+y)=1，==>x+y=2k*pi+pi/2 (k是整数）
sin(2y+x)=sin[2(x+y)-x]=sin(2k*pi+pi-x)
=sinx=1/3