(x²-2y²)²=x⁴-4x²y²+4y⁴
-----------------------------
1. (1) --- x≥0 ; (2) --- x = -3 ∅
2. (1) --- x²-3x+2≠0 ≡ (x-1)(x-2)≠0 ≡ x≠1 ; x≠2
(2) --- x=1 ; x=2 ∅
3. (1) --- x(x²-3x+2) = 0 (2) ⇒ (1)
4. (1) --- x≠1 ; (2) --- x=1 ∅
5. (1) --- x≠1 ; (2) --- x=1 ∅
6. (1) --- (2) ⇒ (1)
7. ⇔
8. ⇔
9. (1) ⇒ (2)
10. ⇔
11. (1) ⇒ (2)
12. (1) ⇒ (2)
2sinx*cosx=sin2x
2.5*2sin11π/12*cos11π/12=2.5*sin11π/6=2.5*sin(10π/6+π/6)=
=-2.5sin π/6 = -2.5*1/2= -1.25
![\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)