f(x)=1/2*(sin²x+cos²x)+1/2*cos²x+√3/4*sin2x
=1/2+1/2*(1+cos2x)/2+√3/4*sin2x
=3/4+1/2*(sin2x*√3/2+cos2x*1/2)
=3/4+1/2*sin(2x+π/3)
则sin)2x+π/3)=±1是最值
所以
{x|x=kπ-5π/12},最小值是1/4
{x|x=kπ+π/12},最大值是5/4
f(x)=1/2*(sin²x+cos²x)+1/2*cos²x+√3/4*sin2x
=1/2+1/2*(1+cos2x)/2+√3/4*sin2x
=3/4+1/2*(sin2x*√3/2+cos2x*1/2)
=3/4+1/2*sin(2x+π/3)
则sin)2x+π/3)=±1是最值
所以
{x|x=kπ-5π/12},最小值是1/4
{x|x=kπ+π/12},最大值是5/4