Question

Доказать тождество:
$frac{ sin( alpha ) + cos( alpha ) }{ sqrt{2} } = cos( alpha - binom{pi}{4} )$

Answer 1

$ttdisplaystyle frac{sin(alpha) + cos(alpha)}{sqrt{2}}=cos(alpha)cdot cosbigg(frac{pi}{4}bigg) + sin(alpha)cdot sinbigg(frac{pi}{4}bigg)\\\frac{sin(alpha) + cos(alpha)}{sqrt{2}} = frac{sqrt{2}cdot cos(alpha)}{2}+frac{sqrt{2}cdot sin(alpha)}{2}~~~~~~~~~~~~~~bigg | cdot (sqrt{2})\\\sin(alpha) + cos(alpha) = frac{2cdot cos(alpha)}{2} + frac{2cdot sin(alpha)}{2}\\\sin(alpha) + cos(alpha) = cos(alpha) + sin(alpha)$