Question

Докажите cos84+cos36-cos24=0

Answer 1

Доказательство:

cos84° + cos36° - cos24° =

2сos((84°+36°)/2) • сos((84°-36°)/2) - cos24° = 2сos(120°/2) • сos(48°/2) - cos24° = 2сos60°• сos24° - cos24° = 2•1/2• сos24° - cos24° = сos24° - cos24° = 0.

0 = 0, равенство доказано.