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