(Sin x + Cos x)^{2}=1+Sin x Cos x

Объяснение:

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