cosx cos2x cos4x cos8x cos16x cos32x =
= (2sinxcosx / 2sinx) cos2x cos4x cos8x cos16x cos32x =
= (sin2x / 2sinx) cos2x cos4x cos8x cos16x cos32x =
= (sin2x / 2sinx) (2sin2xcos2x / 2sin2x) cos4x cos8x cos16x cos32x =
= (sin4x / 4sinx) (2sin4xcos4x / 2sin4x) cos8x cos16x cos32x =
= (sin8x / 8sinx) (2sin8xcos8x / 2sin8x) cos16x cos32x =
= (sin16x / 16sinx) (2sin16xcos16x / 2sin16x) cos32x =
= (sin32x / 32sinx) (2sin32xcos32x / 2sin32x) =
= sin64x / 64sinx
x = π/9
![\frac{sin\frac{64\pi}{9}}{64sin\frac{\pi}{9}}=\frac{sin(7\pi+\frac{\pi}{9})}{64sin\frac{\pi}{9}}= \frac{sin7\pi cos\frac{\pi}{9}+cos7\pi sin\frac{\pi}{9}}{64sin\frac{\pi}{9}} = \frac{-sin\frac{\pi}{9}}{64sin\frac{\pi}{9}} = -\frac{1}{64}](https://tex.z-dn.net/?f=%5Cfrac%7Bsin%5Cfrac%7B64%5Cpi%7D%7B9%7D%7D%7B64sin%5Cfrac%7B%5Cpi%7D%7B9%7D%7D%3D%5Cfrac%7Bsin%287%5Cpi%2B%5Cfrac%7B%5Cpi%7D%7B9%7D%29%7D%7B64sin%5Cfrac%7B%5Cpi%7D%7B9%7D%7D%3D%20%5Cfrac%7Bsin7%5Cpi%20cos%5Cfrac%7B%5Cpi%7D%7B9%7D%2Bcos7%5Cpi%20sin%5Cfrac%7B%5Cpi%7D%7B9%7D%7D%7B64sin%5Cfrac%7B%5Cpi%7D%7B9%7D%7D%20%3D%20%5Cfrac%7B-sin%5Cfrac%7B%5Cpi%7D%7B9%7D%7D%7B64sin%5Cfrac%7B%5Cpi%7D%7B9%7D%7D%20%3D%20-%5Cfrac%7B1%7D%7B64%7D)
1. X² = 49
X = +-7
2.X² = -36
X ∈ ∅
3. X = 0
4. X² = 144
X = +- 12
5. [X = 0
[X = -13
6. X = 0
7. X = +-√15
8. X² = +-√13
9.X = +-6
интеграл от 0 до п/2(1-2sin^2(2x))dx= интеграл от 0 до п/2(cos^2(2x)-sin^2(2x))dx= интеграл от 0 до п/2(cos(4x))dx= 1/4*(sin(4x)) от 0 до п/2=1/4*(0-0)=0
5x - 7xy + 4xy = 5x - 3xy = x(5-3y)
По т. Пифагора находим вторую сторону
b=√13²-5²=12
S=ab=5*12=60