Tgx = 1-√2
1-tgx=√2
tgπ/4 - tgx=√2 ; tgα-tgβ = sin(α-β)/cosαcosβ
sin(45-x)/(cos45·cosx =√2
sin(45-x)[√2/2·cosx] = √2 ⇔ sin(45-x)/cosx = √2·√2/2 =1
sin(45 - x)= cosx
cos(90-(45-x)) -cosx=0
cos(45+x) - cosx =0
-2sin[(45+2x)/2] ·sin(45/2) =0 ⇒
sin(π/8 +x) =0
π/8 +x = πk ; k ∈ Z
x = -π/8 +πk ; k ∈ Z