2. Докажите равенство sin 200° + sin 100° = sin 40°.

sin 200° + sin 100° = 2 sin((200°+100°)/2) cos((200°-100°)/2) = 2 sin(150°) cos(50°)

sin(150°) = sin(180°-30°) = sin(30°) = 1/2

2 * (1/2) * cos(50°) = cos(50°) = sin(90°-50°) = sin(40°)

Доказано.