cos2x/根号2cos(x+π/4)=1/5,0

(cos2x)/√2cos(x＋π/4)＝(cos²x－sin²x)/[√2(cosxcos(π/4)－sinxsin(π/4))]＝[(cosx＋sinx)(cosx－sinx)]/(cosx－sinx)＝cosx＋sinx＝1/5即可.

cos2x/√2cos(x+π/4)=1/5
(cos^2x-sin^2x)/(cosx-sinx)=1/5
(cosx-sinx)(cosx+sinx)/(cosx-sinx)=1/5
cosx+sinx=1/5
5cosx=1-5sinx , 25cos^2x=1-10sinx+25sin^2x,=25-25sin^2x ,50sin^2x -10sinx-24=0
(5sinx-4)(5sinx+3)=0 , 0tanx=±4/3