# Prove that Sin(pi/4 + x) + sin (pi/4 - x) = root 2 cos x ?

LHS=sin(45°+x)+sin(45°-x)
$= 2 \sin \left(\frac{45 + x + 45 - x}{2}\right) \cdot \cos \left(\frac{45 + x - 45 + x}{2}\right)$
$= 2 \cdot \sin 45 \cdot \cos x$
$= \left(\sqrt{2} \cdot \cancel{\sqrt{2}}\right) \cdot \left(\frac{1}{\cancel{\sqrt{2}}}\right) \cos x = \sqrt{2} \cos x = R H S$