Question

已知cos(α+π/4)=-4/5,0

Answer 1

楼主的问题本身有问题!
因为：0＜α＜π/2
所以：α是第一象限角,sinα＞0、cosα＞0
(sinα)^2+(cosα)^2=1
sinα=√[1-(cosα)^2]
cos(α+π/4)=-4/5
cosαcos(π/4)-sinαsin(π/4)=-4/5
cosα(√2)/2-sinα(√2)/2=-4/5
cosα-sinα=-(4/5)√2
cosα-√[1-(cosα)^2]=-(4/5)√2
cosα+(4/5)√2=√[1-(cosα)^2]
(cosα)^2+[(8√2)/5]cosα+32/25=1-(cosα)^2
2(cosα)^2+[(8√2)/5]cosα+7/25=0
cosα={-[(8√2)/5±√{[(8√2)/5]^2-56/25}}/4
={-[(8√2)/5]±6(√2)/5}/4
=-(√2)/10
cosα1=-(√2)/10
cosα2=-(7√2)/10
可见：cosα＜0,这与已知0＜α＜π/2相矛盾
因此：楼主的问题本身有问题!