f(x)=(sinx)^2+cosx
=1-(cosx)^2+cosx
=-(cosx)^2+cosx+1
设t=cosx |x|≤π/4 √2/2≤t≤1
y=-t^2+t+1
=-(t-1/2)^2+5/4
在[√2/2,1]单调递减
取最小值时 t=1 y=1