已知cosx=1/7,cos(x-y)=13/14.且0＜y＜x＜π/2.求y.

已知cosx=1/7,cos(x-y)=13/14.且0＜y＜x＜π/2.求y.
已知cosx=1/7,cos(x-y)=13/14.且0＜y＜x＜π/2.
求y.

已知cosx=1/7,cos(x-y)=13/14.且0＜y＜x＜π/2.求y.
因为0＜y＜x＜π/2,(sin x)^2+(cos x)^2=1
所以sin x=(4*3^(1/2))/7
cos(x-y)=cos(y-x)=13/14
又-π/2<-x所以sin(y-x)=-(3*3^(1/2))/14
sin y=sin((y-x)+x)=sin(y-x)cosx + sinxcos(y-x)=3^(1/2)/2
所以 y=π/3