Задача 72340 (cos(11Pi/12) - cos(Pi/12)) /...

64d2562605b5eb3b135f55a9

08.08.2023 19:21:29

(cos(11Pi/12) - cos(Pi/12)) / sin(5Pi/12)

626fab9a354ab65fb2f43abb

09.08.2023 14:00:38

★

[m]\frac{cos(\frac{11\pi}{12}) - cos(\frac{\pi}{12})}{sin(\frac{5\pi}{12})}[/m]
Есть формула:
[m]cos(a)-cos(b) = -2sin\frac{a+b}{2} \cdot sin\frac{a-b}{2}[/m]
В нашем случае:
[m]cos(\frac{11\pi}{12})-cos(\frac{\pi}{12}) = -2sin(\frac{11\pi+\pi}{24}) \cdot sin(\frac{11\pi-\pi}{24}) =[/m]
[m]= -2sin(\frac{12\pi}{24}) \cdot sin(\frac{10\pi}{24}) = -2 \cdot 1 \cdot sin(\frac{5\pi}{12}) = -2sin(\frac{5\pi}{12})[/m]
Подставляем:
[m]\frac{cos(\frac{11\pi}{12}) - cos(\frac{\pi}{12})}{sin(\frac{5\pi}{12})} = \frac{-2sin(\frac{5\pi}{12})}{sin(\frac{5\pi}{12})} = -2[/m]
Ответ: -2