Question

Упростите выражение 20 б

Answer 1

$sina-\sqrt2\, sin(a-\frac{\pi}{4})=\\\\=sina-\sqrt2\cdot (sina\cdot cos\frac{\pi}{4}-cosa\cdot sin\frac{\pi}{4})=\\\\=sina-\sqrt2\cdot (\frac{\sqrt2}{2}\cdot sina-\frac{\sqrt2}{2}\cdot cosa)=\\\\=sina-sina+cosa=cosa$