Question

sin(pi/4-a)-sin(pi/4+a)=√2cos(pi/2+a)

Answer 1

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