sinx + cosx = -1
<=> [tex]\frac{\sqrt{2}}{2}[/tex].sinx + [tex]\frac{\sqrt{2}}{2}[/tex].cosx = [tex]-\frac{\sqrt{2}}{2}[/tex]
<=> cos([tex]\frac{\pi}{4}[/tex])sinx + sin([tex]\frac{\pi}{4}[/tex])cosx = [tex]-\frac{\sqrt{2}}{2}[/tex]
<=> sin(x+[tex]\frac{\pi}{4}[/tex]) = [tex]-\frac{\sqrt{2}}{2}[/tex]