(sin x + cos x)^2=1+sin x * cos x решить

Sin^2x + 2sinx*cosx + cos^2x = 1 + sinx*cosx
1 + 2sinx*cosx = 1 + sinx*cosx
2sinx*cosx - sinx*cosx = 0 
sinx*cosx = 0 

1) sinx = 0 
x = pik, k ∈ Z

2) cosx = 0 
x = pi/2+ pik, k∈Z