Решите уравнение: (sin x + cos x) = 1+ sin x

sin^2x+cos^2x+2sinxcosx=1+sinxcosx

1+2sinxcosx=1+sinxcosx

sinxcosx=0

sinx=0

x=пn , nZ

cosx=0

x=п/2 +пn, nZ

x=пn/2

(sin x + cos x) = 1+ sin x cos x

sin x +2sin x cos x+cos x=1+sin x cos x

1+sin 2x =1+sin x cos x

sin 2x=sin x cos x

sin 2x-sin x cos x=0

2 sin x cos x - sin x cos x=0

sin x cos x=0

sin x=0 cos x=0

x=k, kZ x=/2 +k, kZ

x=k/2, kZ