<span>2cos2x = √3sin(3Π/2+x)
</span><span>2cos2x = -√3cosx
</span>cosx(2cosx +√3)=0cosx=0
x=п/2+пk<span>cosx=-√3/2
x=±(п-п/6)+2пn=±5п/6+2пn k,n €Z</span>
![1)\frac{1}{9} x\geq-1\\\frac{1}{9}x*9 \geq-1*9\\x\geq -9](https://tex.z-dn.net/?f=1%29%5Cfrac%7B1%7D%7B9%7D+x%5Cgeq-1%5C%5C%5Cfrac%7B1%7D%7B9%7Dx%2A9+%5Cgeq-1%2A9%5C%5Cx%5Cgeq+-9)
x ∈ [- 9 ; + ∞)
2)3 - 8x < 0
- 8x < - 3
x > 0,375
x ∈ (0,375 ; + ∞)
3) 1,4 - 4(2x + 1) > 1,8 - 3x
1,4 - 8x - 4 > 1,8 - 3x
- 8x + 3x > 1,8 - 1,4 + 4
- 5x > 4,4
x < - 0,88
x ∈ (- ∞ ; - 0,88)
![4)\frac{4-a}{3}> \frac{5-3a}{5}\\\frac{4-a}{3}*15> \frac{5-3a}{5}*15\\5(4-a)>3(5-3a)\\20-5a>15-9a\\-5a+9a>15-20\\4a>-5\\a>-1,25](https://tex.z-dn.net/?f=4%29%5Cfrac%7B4-a%7D%7B3%7D%3E+%5Cfrac%7B5-3a%7D%7B5%7D%5C%5C%5Cfrac%7B4-a%7D%7B3%7D%2A15%3E+%5Cfrac%7B5-3a%7D%7B5%7D%2A15%5C%5C5%284-a%29%3E3%285-3a%29%5C%5C20-5a%3E15-9a%5C%5C-5a%2B9a%3E15-20%5C%5C4a%3E-5%5C%5Ca%3E-1%2C25)
a ∈ (- 1,25 ; + ∞)
Преобразуем выражение в скобках:
![\frac{\sqrt{q}}{p-\sqrt{pq}}+\frac{\sqrt{p}}{q-\sqrt{pq}}=\frac{\sqrt{q}}{\sqrt{p}(\sqrt{p}-\sqrt{q})}+\frac{\sqrt{p}}{-\sqrt{q}(\sqrt{p}-\sqrt{q})}=\\=\frac{q-p}{\sqrt{q}\sqrt{p}(\sqrt{p}-\sqrt{q})}=\frac{-(p-q)}{\sqrt{q}\sqrt{p}(\sqrt{p}-\sqrt{q})}](https://tex.z-dn.net/?f=%5Cfrac%7B%5Csqrt%7Bq%7D%7D%7Bp-%5Csqrt%7Bpq%7D%7D%2B%5Cfrac%7B%5Csqrt%7Bp%7D%7D%7Bq-%5Csqrt%7Bpq%7D%7D%3D%5Cfrac%7B%5Csqrt%7Bq%7D%7D%7B%5Csqrt%7Bp%7D%28%5Csqrt%7Bp%7D-%5Csqrt%7Bq%7D%29%7D%2B%5Cfrac%7B%5Csqrt%7Bp%7D%7D%7B-%5Csqrt%7Bq%7D%28%5Csqrt%7Bp%7D-%5Csqrt%7Bq%7D%29%7D%3D%5C%5C%3D%5Cfrac%7Bq-p%7D%7B%5Csqrt%7Bq%7D%5Csqrt%7Bp%7D%28%5Csqrt%7Bp%7D-%5Csqrt%7Bq%7D%29%7D%3D%5Cfrac%7B-%28p-q%29%7D%7B%5Csqrt%7Bq%7D%5Csqrt%7Bp%7D%28%5Csqrt%7Bp%7D-%5Csqrt%7Bq%7D%29%7D)
![\frac{-(p-q)}{\sqrt{q}\sqrt{p}(\sqrt{p}-\sqrt{q})}*\frac{p\sqrt{q}+q\sqrt{p}}{p-q}=-\frac{\sqrt{p}\sqrt{q}(\sqrt{p}+\sqrt{q})}{\sqrt{q}\sqrt{p}(\sqrt{p}-\sqrt{q})}=-\frac{\sqrt{p}+\sqrt{q}}{\sqrt{p}-\sqrt{q}}=\\=-\frac{\sqrt{36}+\sqrt{4}}{\sqrt{36}-\sqrt{4}}=-\frac{8}{6}=-\frac{4}{3}](https://tex.z-dn.net/?f=%5Cfrac%7B-%28p-q%29%7D%7B%5Csqrt%7Bq%7D%5Csqrt%7Bp%7D%28%5Csqrt%7Bp%7D-%5Csqrt%7Bq%7D%29%7D%2A%5Cfrac%7Bp%5Csqrt%7Bq%7D%2Bq%5Csqrt%7Bp%7D%7D%7Bp-q%7D%3D-%5Cfrac%7B%5Csqrt%7Bp%7D%5Csqrt%7Bq%7D%28%5Csqrt%7Bp%7D%2B%5Csqrt%7Bq%7D%29%7D%7B%5Csqrt%7Bq%7D%5Csqrt%7Bp%7D%28%5Csqrt%7Bp%7D-%5Csqrt%7Bq%7D%29%7D%3D-%5Cfrac%7B%5Csqrt%7Bp%7D%2B%5Csqrt%7Bq%7D%7D%7B%5Csqrt%7Bp%7D-%5Csqrt%7Bq%7D%7D%3D%5C%5C%3D-%5Cfrac%7B%5Csqrt%7B36%7D%2B%5Csqrt%7B4%7D%7D%7B%5Csqrt%7B36%7D-%5Csqrt%7B4%7D%7D%3D-%5Cfrac%7B8%7D%7B6%7D%3D-%5Cfrac%7B4%7D%7B3%7D)
Sint/cost≤0
tgt≤0
t∈(-π/2+πn;πn]