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