函数y=(sin^2x+1)(cos^2+3)的最大值是A4B21/4C6D25/4

函数y=(sin^2x+1)(cos^2+3)的最大值是A4B21/4C6D25/4
函数y=(sin^2x+1)(cos^2+3)的最大值是
A4
B21/4
C6
D25/4

函数y=(sin^2x+1)(cos^2+3)的最大值是A4B21/4C6D25/4
选C 6
y=(sin²x+1)(cos²x+3)=sin²xcos²x+3sin²x+cos²x+3=sin²xcos²x+2sin²x+4=sin²x(1-sin²x)+2sin²x+4
=-sin^4x+3sin²x+4=25/4-(sin^4x-3sin²x+9/4)=25/4-(3/2-sin²x)²

选C6
y=(sin²x+1)(cos²x+3)=(sin²x+1)(4-sin²x)
=-sin^4x+3sin²x+4
=25/4-(sin^4x-3sin²x+9/4)
=25/4-(3/2-sin²x)²≤25/4-(3/2-1)²=6