Question

$\frac{4 \sin(20) \sin(50) \sin(70) }{ \sin(80) }$
Помогите с примером! Пожалуйста!
В ответе должно получиться ровно 1. За ранее благодарю.​

Answer 1

$\frac{4sin(20^{\circ})sin(50^{\circ})sin(70^{\circ})}{sin(80^{\circ})}=\frac{4sin(20^{\circ})sin(50^{\circ})sin(90^{\circ}-20^{\circ})}{sin(80^{\circ})}=\\=\frac{2sin(40^{\circ})sin(50^{\circ})}{sin(80^{\circ})}=\frac{2sin(90^{\circ}-40^{\circ})sin(40^{\circ})}{sin(80^{\circ})}=\frac{2cos(40^{\circ})sin(40^{\circ})}{sin(80^{\circ})}=1$