Решить уравнение tg (x) = 1 - (корень из 2)

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