Question

Преобразовать в произведение 1-2sina

Answer 1

$1-2sin \alpha =2\cdot \frac{1}{2}-2sin \alpha =2\cdot sin\frac{\pi}{6}-2sin \alpha =\\\\=2\cdot (sin\frac{\pi}{6}-sin \alpha )=2\cdot 2sin\frac{\frac{\pi}{6}- \alpha }{2}\cdot cos\frac{\frac{\pi}{6}+ \alpha }{2}=\\\\=4\cdot sin(\frac{\pi}{12}-\frac{ \alpha }{2})\cdot cos(\frac{\pi}{12}+ \frac{ \alpha }{2})$