(1) 向量m+向量n=(√2+cosα-sinα,sinα+cosα)
│向量m+向量n│=√[(√2+cosα-sinα)²+(sinα+cosα)²]
=√[4+4sin(π/4-α)]
(2) 当│向量m+向量n│=8根号2/5时
则4+4sin(π/4-α)=128/25
sin(π/4-α)=7/25 cos(α+π/4)=7/25
已知α属于π到2π
a/2+π/8∈[5π/8,9π/8] 即cos(a/2+π/8)
(1) 向量m+向量n=(√2+cosα-sinα,sinα+cosα)
│向量m+向量n│=√[(√2+cosα-sinα)²+(sinα+cosα)²]
=√[4+4sin(π/4-α)]
(2) 当│向量m+向量n│=8根号2/5时
则4+4sin(π/4-α)=128/25
sin(π/4-α)=7/25 cos(α+π/4)=7/25
已知α属于π到2π
a/2+π/8∈[5π/8,9π/8] 即cos(a/2+π/8)