(sinx+cosx)^2=sinx+cosx Решите

(sinx+cosx)²-(sinx+cosx)=0(sinx+cosx)*((sinx+cosx)-1)=0sinx+cosx=0/cosxtgx+1=0tgx=-1x=-π/4+πk,k∈zsinx+cosx-1=02sinx/2cosx/2+cos²x/2-sin²x/2-sin²x/2-cos²x/2=02sinx/2cosx/2-2sin²x/2=02sinx/2(cosx/2-sinx/2)=0sinx/2=0x/2=πkx=2πk,k∈zcosx/2-sinx/2=0/cosx/21-tgx/2=0tgx/2=1x/2=π/4+πkx=π/2+2πk,k∈z