y的最大值是3/2. 说明如下:
y=(cosA)^2+(cosB)^2=(1/2)[2(cosA)^2+2(cosB)^2]
=(1/2)[(1+cos2A)+(1+cos2B)]=1+(1/2)(cos2A+cos2B)
=1+cos(A+B)cos(A-B)=1+cos60°cos(A-B)=1+(1/2)cos(A-B).
∴当cos(A-B)=1,即A=B时,y有最大值,且最大值为1+1/2=3/2.
y的最大值是3/2. 说明如下:
y=(cosA)^2+(cosB)^2=(1/2)[2(cosA)^2+2(cosB)^2]
=(1/2)[(1+cos2A)+(1+cos2B)]=1+(1/2)(cos2A+cos2B)
=1+cos(A+B)cos(A-B)=1+cos60°cos(A-B)=1+(1/2)cos(A-B).
∴当cos(A-B)=1,即A=B时,y有最大值,且最大值为1+1/2=3/2.