Sinx+cosx=-1 решите уравнение

2sin (x/2) cos (x/2) + cos² (x/2) - sin² (x/2) + sin² (x/2) + cos² (x/2) = 0

2sin (x/2) cos (x/2) + 2cos² (x/2) = 0

2cos (x/2) * (sin (x/2) + cos (x/2)) = 0

cos (x/2) = 0⇒x/2=π/2+πn⇒x=π+2πn, n∈z

sin (x/2) + cos (x/2) = 0/cos (x/2)

tg (x/2) + 1=0⇒tg (x/2) = - 1⇒x/2=-π/4+πk⇒x=π/2+2πk, k∈z