求函数y=sin^2 x+3cos^2 x最小正周期及最值当取最大值和最小值时x的集合?

题目

求函数y=sin^2 x+3cos^2 x最小正周期及最值当取最大值和最小值时x的集合?

答案

y=sin^2 x+3cos^2 x
=sin^2x+cos^2x+2cos^2x
=1+1+cos2x
=2+cos2x
T=2π/2=π
取最大值x=2kπ
取最小值时x=2kπ+π