Решить уравнение : √2 cos(x-pi/4)=(sinx+cosx)^2

√2cosxcosπ/4+√2sinxsinπ/4=(sinx+cosx)²
√2*√2/2cosx+√2*√2/2sinx=(sinx+cosx)²
cosx+sinx=(sinx+cosx)²
(sinx+cosx)(sinx+cosx-1)=0
sinx+cosx=0
sinx+sin(π/2-x)=0
2sinπ/4cos(x-π/4)=0
cos(x-π/4)=0
x-π/4=π/2+πn
x=3π/4+ππn
sinx+cosx-1=0
2sinx/2cosx/2+cos²x/2-sin²x/2-sin²x/2-cos²x/2=0
2sinx/2cosx/2-2sin²x/2=0/2cos²x/2≠0
tgx/2-tg²x/2=0
tgx/2(1-tgx/2)=0
tgx/2=0
x/2=πn
x=2πn
tgx/2=1
x/2=π/4+πn
x=π/2+2πn