Question

Sin(pi/4-a)-sin(pi/4+a)=√2cos(pi/2+a)

Answer 1

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