Решите пожалуйста sinx-cosx=1

sinx-cosx=1 2sin(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)=0 cos(x/2)(cos(x/2)-sin(x/2))=0 cos(x/2)=0 x/2=π/2+πn x=π+2πn cos(x/2)-sin(x/2)=0 cos(x/2)=sin(x/2)  I÷sin(x/2)    sin(x/2)≠0  x≠2πn ctg(x/2)=1  x/2=π/4+2πn   x=5π/4+2πn x=π/2+4πn   x=5π/2+4πn Ответ: х=π/2+2πn   x=π+2πn.