Преобразуйте в произведение Cos 65' + cos 55'

Question

Преобразуйте в произведение
Cos 65' + cos 55'

Answer 1

Cosa+cosb=2cos[(a+b)/2]*cos[(a-b)/2]
cos65+cos55=2cos60*cos5=2*1/2*cos5=cos5

Answer 2

Преобразуем по формуле:
cosA + cosB = 2cos[(A + B)/2]·cos[(A - B)/2]
cos65° + cos55° = 2cos[(65° + 55°)/2]·cos[(65° - 55°)/2] = 2cos(120°/2)·cos(10°/2) = 2·cos60°·cos5° = 2·1/2·cos5° = cos5°.