cos2x/根号2cos(x+π/4)=1/5,0

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cos2x/根号2cos(x+π/4)=1/5,0
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cos2x/根号2cos(x+π/4)=1/5,0
cos2x/根号2cos(x+π/4)=1/5,0

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