Решить уравнение

tgx + 1=sinx + cosx

Sinx/cosx + 1=sinx+cosx

(sinx+cosx) / cosx - (sinx+cosx) = 0

(Sinx+cosx) (1-cosx) = 0 cosx≠0

sinx+cosx=0

sinx+sin (π/2-x) = 0

2sinπ/4cos (π/4-x) = 0

cos (π/4-x) = 0⇒π/4-x=π/2+2πn⇒x=π/4-π/2+2πn=-π/4+2πn

1-cosx=0⇒cosx=1⇒x=2πn