Sin(pi/4-a)-sin(pi/4+a)=√2cos(pi/2+a)

[latex]sin(\frac{ \pi}{4}-a)-sin(\frac{ \pi}{4}+a)= \sqrt{2}*cos(\frac{ \pi}{2}+a)[/latex] [latex]sin\frac{ \pi}{4}*cosa-cos\frac{ \pi}{4}*sina-(sin\frac{ \pi}{4}*cosa+cos\frac{ \pi}{4}*sina)=-\sqrt{2}*sina[/latex] [latex]-2cos\frac{ \pi}{4}*sina=-\sqrt{2}*sina[/latex] [latex]-2* \frac{ \sqrt{2}}{2}*sina=-\sqrt{2}*sina[/latex] [latex]-\sqrt{2}=-\sqrt{2}[/latex] - верно при любых а