函数y=(sin^2+1)(cos^2+3)函数y=(sin^2+1)(cos^2+3)的最大值是？

函数y=(sin^2+1)(cos^2+3)函数y=(sin^2+1)(cos^2+3)的最大值是？
函数y=(sin^2+1)(cos^2+3)
函数y=(sin^2+1)(cos^2+3)
的最大值是？

函数y=(sin^2+1)(cos^2+3)函数y=(sin^2+1)(cos^2+3)的最大值是？
y=(sin^2+1)(cos^2+3)
=sin^2·cos^2+3sin^2+cos^2+3
=sin^2·cos^2+2sin^2+（sin^2+cos^2）+3
=sin^2·cos^2+2sin^2+4, 因为sin^2+cos^2=1,移项,cos^2=1-sin^2
=sin^2（1-sin^2）+2sin^2+4
= -（sin^2)^2+3sin^2+4
即求F(x）=-x^2+3x+4 ,（0≤x≤1,因为0≤sin^2≤1）的最大值
二次函数因该会吧?F(x）最大=F（1）=6,
即y=(sin^2+1)(cos^2+3)最大值是6,当sin^2=1,cos^2=0时取得