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)²cosx+sinx=(sinx+cosx)²(sinx+cosx)(sinx+cosx-1)=0sinx+cosx=0sinx+sin(π/2-x)=02sinπ/4cos(x-π/4)=0cos(x-π/4)=0x-π/4=π/2+πnx=3π/4+ππnsinx+cosx-1=02sinx/2cosx/2+cos²x/2-sin²x/2-sin²x/2-cos²x/2=02sinx/2cosx/2-2sin²x/2=0/2cos²x/2≠0tgx/2-tg²x/2=0tgx/2(1-tgx/2)=0tgx/2=0x/2=πnx=2πntgx/2=1x/2=π/4+πnx=π/2+2πn