<span>sinx/2*sin3x/2=1/2
1/2[cos(x/2 - 3x/2) - cos(x/2 + 3x/2)] = 1/2
cos(x) - cos(2x) = 1
применяем формулу: (cos2x = 2</span>cos²x - 1)<span>
2cos</span>²x - cosx = 0
cosx(2cosx - 1) = 0
1) cosx = 0
x₁ = π/2 + πk, k∈Z
2) 2cosx - 1 = 0
cosx = 1/2
x = (+ -)arccos(1/2) + 2πn, n∈Z
x₂ = (+ -)(π/3) + 2πn, n∈Z
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Решение смотри в приложениях
![y = x*\frac{46}{5} - (x-5)*\frac{6}{5}\\\\ y(0) = 0 - (-5)*\frac{6}{5} = 6\\\\ y(5) = 5*\frac{46}{5} - 0 = 46](https://tex.z-dn.net/?f=y+%3D+x%2A%5Cfrac%7B46%7D%7B5%7D+-+%28x-5%29%2A%5Cfrac%7B6%7D%7B5%7D%5C%5C%5C%5C+y%280%29+%3D+0+-+%28-5%29%2A%5Cfrac%7B6%7D%7B5%7D+%3D+6%5C%5C%5C%5C+y%285%29+%3D+5%2A%5Cfrac%7B46%7D%7B5%7D+-+0+%3D+46)
Уравнение можно преобразовать к такому виду:
![y = x*\frac{46}{5} - (x-5)*\frac{6}{5} | * 5\\\\ 5y = 46x - 6(x-5)\\\\ 5y = 40x +30 | : 5\\\\y = 8x + 6](https://tex.z-dn.net/?f=+y+%3D+x%2A%5Cfrac%7B46%7D%7B5%7D+-+%28x-5%29%2A%5Cfrac%7B6%7D%7B5%7D+%7C+%2A+5%5C%5C%5C%5C+5y+%3D+46x+-+6%28x-5%29%5C%5C%5C%5C+5y+%3D+40x+%2B30+%7C+%3A+5%5C%5C%5C%5Cy+%3D+8x+%2B+6)
Первоначальное уравнение было найденно таким способом:
![y = (x - x_1)\frac{y_2}{x_2-x_1} + (x - x_2)\frac{y_1}{x_1-x_2}](https://tex.z-dn.net/?f=y+%3D+%28x+-+x_1%29%5Cfrac%7By_2%7D%7Bx_2-x_1%7D+%2B+%28x+-+x_2%29%5Cfrac%7By_1%7D%7Bx_1-x_2%7D)