It is known that 0 < α < π / 4, β is the minimum positive period of F (x) = cos (2x + π / 8), and vector a = (Tan (α + 1 / 4 β) Given that 0 〈α 〈π / 4, β is the minimum positive period of F (x) = cos (2x + π / 8), vector a = Tan (α + 1 / 4 β), - 1), B = (COS α, 2), and a · B = m, find the value of 2cos α Λ 2 + sin2 (α + β) / cos α - sin α

It is known that 0 < α < π / 4, β is the minimum positive period of F (x) = cos (2x + π / 8), and vector a = (Tan (α + 1 / 4 β) Given that 0 〈α 〈π / 4, β is the minimum positive period of F (x) = cos (2x + π / 8), vector a = Tan (α + 1 / 4 β), - 1), B = (COS α, 2), and a · B = m, find the value of 2cos α Λ 2 + sin2 (α + β) / cos α - sin α

f(x)=cos(2x+π/8)
T=2π/2=π=β
tan(α+β/4)=sin(α+β/4)/cos(α+β/4)
ab=sin(α+β/4)cosα/cos(α+β/4) -2
=（sinα+cosα)cosα/(cosα-sinα) -2
=(sin2α+2cos^2α)/2(cosα-sinα)-2=m
(2cos^2α+sin2α)/(cosα-sinα)=2m+4
[2cos^2α+sin2(α+β)]/(cosα-sinα)
=[2cos^2α+sin(2α+2π)]/(cosα-sinα)
=(2cos^2α+sin2α)/(cosα-sinα)
=2m+4