f(x)=2cosx+(sinx)^2=2cosx+1-(cosx)^2= -(cosx)^2+2cosx+1 (-π/4,π/2]令：t=cosx 因为 (-π/4,π/2],所以 [0,1]原式为：f(t)= -t^2+2t+1 [0,1]f(t)= -t^2+2t+1= -(t-1)^2+2结合定义域可知,当t=0时,取最小值.f(t)m...