已知向量m=(cosx,-sinx)向量n=(√2+sinx,cosx)定义在【0,π】上的函数f(x)|m+n|2-4

向量m+n=(√2+sinx+cosx,cosx-sinx)=√2 (1+sin(x+π/4),-sin(x-π/4))=√2 (1+sin(x+π/4),cos(x+π/4))f(x)=2[(1+sin(x+π/4))^2+cos^2(x+π/4)]-4=4[1+sin(x+π/4) ]-4。= 4sin(x+π/4)x+π/4∈[π/4,5π/4](1)当x=π/4时,f max=4,当x=5π/4时f min=-2√2。(2) sin(x+π/4)= √2/4,0