-24х+15+56х+30
(56-24)х+45
-30х+45
45-30х
Ты л1о1х максим лолололололололол лололол
2sin15° *(cos10° *cos5°-sin10° *sin5°)=2sin15° *cos(10°+5°)=
=2sin15° *cos15°=sin(2*15°)=sin30°=1/2=0,5
Представим котангенс в числителе в виде
![\cot\left(\frac{13\pi}{10}\right)=\cot\left(\frac{15\pi}{10}-\frac{2\pi}{10}\right)](https://tex.z-dn.net/?f=%5Ccot%5Cleft%28%5Cfrac%7B13%5Cpi%7D%7B10%7D%5Cright%29%3D%5Ccot%5Cleft%28%5Cfrac%7B15%5Cpi%7D%7B10%7D-%5Cfrac%7B2%5Cpi%7D%7B10%7D%5Cright%29)
По формуле разности углов котангенсов
![\cot{(\alpha-\beta)}=\frac{\cot\alpha\cot\beta+1}{\cot\beta-\cot\alpha}](https://tex.z-dn.net/?f=%5Ccot%7B%28%5Calpha-%5Cbeta%29%7D%3D%5Cfrac%7B%5Ccot%5Calpha%5Ccot%5Cbeta%2B1%7D%7B%5Ccot%5Cbeta-%5Ccot%5Calpha%7D)
![\cot\left(\frac{15\pi}{10}-\frac{2\pi}{10}\right)=\frac{1+\cot\frac{15\pi}{10}\cot\frac{2\pi}{10}}{\cot\frac{15\pi}{10}-\cot\frac{2\pi}{10}}](https://tex.z-dn.net/?f=%5Ccot%5Cleft%28%5Cfrac%7B15%5Cpi%7D%7B10%7D-%5Cfrac%7B2%5Cpi%7D%7B10%7D%5Cright%29%3D%5Cfrac%7B1%2B%5Ccot%5Cfrac%7B15%5Cpi%7D%7B10%7D%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D%7B%5Ccot%5Cfrac%7B15%5Cpi%7D%7B10%7D-%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D)
![\frac{1+\cot\frac{15\pi}{10}\cot\frac{2\pi}{10}}{\cot\frac{15\pi}{10}-\cot\frac{2\pi}{10}}=\frac{1+0*\cot\frac{2\pi}{10}}{0-\cot\frac{2\pi}{10}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B%5Ccot%5Cfrac%7B15%5Cpi%7D%7B10%7D%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D%7B%5Ccot%5Cfrac%7B15%5Cpi%7D%7B10%7D-%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D%3D%5Cfrac%7B1%2B0%2A%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D%7B0-%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D)
![\frac{1+0*\cot\frac{2\pi}{10}}{0-\cot\frac{2\pi}{10}}=\frac{1}{0-\cot\frac{\pi}{5}}=-\frac{1}{\cot\frac{\pi}{5}}](https://tex.z-dn.net/?f=%5Cfrac%7B1%2B0%2A%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D%7B0-%5Ccot%5Cfrac%7B2%5Cpi%7D%7B10%7D%7D%3D%5Cfrac%7B1%7D%7B0-%5Ccot%5Cfrac%7B%5Cpi%7D%7B5%7D%7D%3D-%5Cfrac%7B1%7D%7B%5Ccot%5Cfrac%7B%5Cpi%7D%7B5%7D%7D)
Теперь подставим, получившееся значение в саму формулу
![-6*\left(-\frac{1}{\cot\frac{\pi}{5}}\right)*\frac{1}{\tan\frac{\pi}{5}}=6*\frac{1}{\cot\frac{\pi}{5}\tan\frac{\pi}{5}}](https://tex.z-dn.net/?f=-6%2A%5Cleft%28-%5Cfrac%7B1%7D%7B%5Ccot%5Cfrac%7B%5Cpi%7D%7B5%7D%7D%5Cright%29%2A%5Cfrac%7B1%7D%7B%5Ctan%5Cfrac%7B%5Cpi%7D%7B5%7D%7D%3D6%2A%5Cfrac%7B1%7D%7B%5Ccot%5Cfrac%7B%5Cpi%7D%7B5%7D%5Ctan%5Cfrac%7B%5Cpi%7D%7B5%7D%7D)
По свойству тангенсов и котангенсов
![\tan\alpha*\cot\alpha=1](https://tex.z-dn.net/?f=%5Ctan%5Calpha%2A%5Ccot%5Calpha%3D1)
Получаем
![6*\frac{1}{\cot\frac{\pi}{5}\tan\frac{\pi}{5}}=6](https://tex.z-dn.net/?f=6%2A%5Cfrac%7B1%7D%7B%5Ccot%5Cfrac%7B%5Cpi%7D%7B5%7D%5Ctan%5Cfrac%7B%5Cpi%7D%7B5%7D%7D%3D6)
Ответ: 6
1) cos²x/2-sin²x/2=0, это косинус двойного угла, cosx=0, x=π/2+πn,n∈Z