Решите пожалуйста sinx-cosx=1

sinx-cosx=12sin(x/2)cos(x/2)-cos²(x/2)+sin²(x/2)=sin²(x/2)+cos²(x/2)2cos²(x/2)-2sin(x/2)cos(x/2)=0cos(x/2)(cos(x/2)-sin(x/2))=0cos(x/2)=0x/2=π/2+πnx=π+2πncos(x/2)-sin(x/2)=0cos(x/2)=sin(x/2)  I÷sin(x/2)    sin(x/2)≠0  x≠2πnctg(x/2)=1 x/2=π/4+2πn   x=5π/4+2πnx=π/2+4πn   x=5π/2+4πnОтвет: х=π/2+2πn   x=π+2πn.