Question

Преобразуйте в произведение 1-√2sin2a​

Answer 1

$1-\sqrt2\, sin2a=\sqrt2\cdot \Big(\dfrac{1}{\sqrt2}-sin2a\Big)=\sqrt2\cdot \Big(sin\frac{\pi}{4}-sin2a\Big)=\\\\\\=\sqrt2\cdot 2\cdot sin\, \dfrac{\frac{\pi}{4}-2a}{2}\cdot cos\, \dfrac{\frac{\pi}{4}+2a}{2} =2\sqrt2\cdot sin\Big(\dfrac{\pi}{8}-a\Big)\cdot cos\Big(\dfrac{\pi}{8}+a\Big)\\\\\\\\\star \; \; sina-sin\beta =2\, sin\frac{a-\beta }{2}\cdot cos\frac{a+\beta }{2}\; \; \star$