1 + sin 2x - sin x = cosx

1 + sin 2x - sin x = cosx

sin^2x + 2sinxcosx + cos^2x - sinx - cosx = 0

(sinx + cosx) ^2 - (sinx + cosx) = 0

(sinx + cosx) * (sinx + cosx - 1) = 0

1) sin x + cos x = 0

tgx + 1 = 0

tgx = - 1

x = - pi/4+pik, k∈Z

2) sinx + cosx = 1

√2*sin (pi/4 + x) = 1

sin (pi/4 + x) = √2/2

pi/4+x=pi/4+2pik

x=pi/4-pi/4+2pik

x=2pik, k∈Z

pi/4+x=3pi/4+2pik

x=3pi/4-pi/4+2pik

x=pi/2+2pik, k∈Z