-0.463647603 rad
надеюсь правильно
Разложим квадратный трехчлена на множители
ах²+bx+c=a(x-x₁)(x-x₂)
D=(-4)²-4·3·(-7)=16+84=100
x₁=(4-10)/6=-1 или x₂=(4+10)/6=7/3
3х²-4x-7 = 3(x- (-1))(x - (7/3))=(3х-7)(х+1)
3х²-4x-7≤0;
(3х-7)(х+1)≤0
Решаем методом интервалов
___+___[-1]___-___[7/3]___+____
О т в е т. [-1; 7/3]
![\tan\alpha+\tan\beta=\tan(\alpha+\beta)*(1-\tan\alpha\tan\beta)](https://tex.z-dn.net/?f=%5Ctan%5Calpha%2B%5Ctan%5Cbeta%3D%5Ctan%28%5Calpha%2B%5Cbeta%29%2A%281-%5Ctan%5Calpha%5Ctan%5Cbeta%29)
![\tan25^0+\tan35^0=\tan(25^0+35^0)*(1-\tan25^0\tan35^0)](https://tex.z-dn.net/?f=%5Ctan25%5E0%2B%5Ctan35%5E0%3D%5Ctan%2825%5E0%2B35%5E0%29%2A%281-%5Ctan25%5E0%5Ctan35%5E0%29)
![\tan25^0+\tan35^0=\tan60^0*(1-\tan25^0\tan35^0)](https://tex.z-dn.net/?f=%5Ctan25%5E0%2B%5Ctan35%5E0%3D%5Ctan60%5E0%2A%281-%5Ctan25%5E0%5Ctan35%5E0%29)
![\tan25^0+\tan35^0=\sqrt{3}*(1-\tan25^0\tan35^0)](https://tex.z-dn.net/?f=%5Ctan25%5E0%2B%5Ctan35%5E0%3D%5Csqrt%7B3%7D%2A%281-%5Ctan25%5E0%5Ctan35%5E0%29)
Отдельно вычислим произведение в скобках по формуле тангенса
![\tan\alpha=\frac{\sin\alpha}{\cos\alpha}](https://tex.z-dn.net/?f=%5Ctan%5Calpha%3D%5Cfrac%7B%5Csin%5Calpha%7D%7B%5Ccos%5Calpha%7D)
![\tan25^0\tan35^0=\frac{\sin25^0\sin35^0}{\cos25^0\cos35^0}](https://tex.z-dn.net/?f=%5Ctan25%5E0%5Ctan35%5E0%3D%5Cfrac%7B%5Csin25%5E0%5Csin35%5E0%7D%7B%5Ccos25%5E0%5Ccos35%5E0%7D)
Воспользуемся формулами произведения синусов и косинусов
![\sin\alpha\sin\beta=\frac{1}{2}*(\cos(\alpha-\beta)-cos(\alpha+\beta))](https://tex.z-dn.net/?f=%5Csin%5Calpha%5Csin%5Cbeta%3D%5Cfrac%7B1%7D%7B2%7D%2A%28%5Ccos%28%5Calpha-%5Cbeta%29-cos%28%5Calpha%2B%5Cbeta%29%29)
![\cos\alpha\cos\beta=\frac{1}{2}*(\cos(\alpha-\beta)+cos(\alpha+\beta))](https://tex.z-dn.net/?f=%5Ccos%5Calpha%5Ccos%5Cbeta%3D%5Cfrac%7B1%7D%7B2%7D%2A%28%5Ccos%28%5Calpha-%5Cbeta%29%2Bcos%28%5Calpha%2B%5Cbeta%29%29)
![\tan25^0\tan35^0=\frac{\cos(25^0-35^0)-\cos(25^0+35^0)}{\cos(25^0-35^0)+\cos(25^0+35^0)}](https://tex.z-dn.net/?f=%5Ctan25%5E0%5Ctan35%5E0%3D%5Cfrac%7B%5Ccos%2825%5E0-35%5E0%29-%5Ccos%2825%5E0%2B35%5E0%29%7D%7B%5Ccos%2825%5E0-35%5E0%29%2B%5Ccos%2825%5E0%2B35%5E0%29%7D)
![\tan25^0\tan35^0=\frac{\cos10^0-\cos60^0}{\cos10^0+\cos60^0}](https://tex.z-dn.net/?f=%5Ctan25%5E0%5Ctan35%5E0%3D%5Cfrac%7B%5Ccos10%5E0-%5Ccos60%5E0%7D%7B%5Ccos10%5E0%2B%5Ccos60%5E0%7D)
![\tan25^0\tan35^0=\frac{\cos10^0-0,5}{\cos10^0+0,5}](https://tex.z-dn.net/?f=%5Ctan25%5E0%5Ctan35%5E0%3D%5Cfrac%7B%5Ccos10%5E0-0%2C5%7D%7B%5Ccos10%5E0%2B0%2C5%7D)
![1-\tan25^0\tan35^0=1-\frac{\cos10^0-0,5}{\cos10^0+0,5}](https://tex.z-dn.net/?f=1-%5Ctan25%5E0%5Ctan35%5E0%3D1-%5Cfrac%7B%5Ccos10%5E0-0%2C5%7D%7B%5Ccos10%5E0%2B0%2C5%7D)
![1-\frac{\cos10^0-0,5}{\cos10^0+0,5}=\frac{\cos10^0+0,5-\cos10^0+0,5}{\cos10^0+0,5}](https://tex.z-dn.net/?f=1-%5Cfrac%7B%5Ccos10%5E0-0%2C5%7D%7B%5Ccos10%5E0%2B0%2C5%7D%3D%5Cfrac%7B%5Ccos10%5E0%2B0%2C5-%5Ccos10%5E0%2B0%2C5%7D%7B%5Ccos10%5E0%2B0%2C5%7D)
![\frac{\cos10^0+0,5-\cos10^0+0,5}{\cos10^0+0,5}=\frac{1}{\cos10^0+0,5}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Ccos10%5E0%2B0%2C5-%5Ccos10%5E0%2B0%2C5%7D%7B%5Ccos10%5E0%2B0%2C5%7D%3D%5Cfrac%7B1%7D%7B%5Ccos10%5E0%2B0%2C5%7D)
![\tan25^0+\tan35^0=\sqrt{3}*\frac{1}{\cos10^0+0,5}](https://tex.z-dn.net/?f=%5Ctan25%5E0%2B%5Ctan35%5E0%3D%5Csqrt%7B3%7D%2A%5Cfrac%7B1%7D%7B%5Ccos10%5E0%2B0%2C5%7D)
![\tan25^0+\tan35^0=\frac{\sqrt{3}}{\cos10^0+0,5}](https://tex.z-dn.net/?f=%5Ctan25%5E0%2B%5Ctan35%5E0%3D%5Cfrac%7B%5Csqrt%7B3%7D%7D%7B%5Ccos10%5E0%2B0%2C5%7D)
Cos(a)+cos(b)=2*cos((a+b)/2)*cos((a-b)/2)