tg3pi/4+2 cos 5 pi/3=
![tg(\frac{3Pi}{4})+2cos(\frac{5Pi}{3})=\\tg(Pi-\frac{Pi}{4})+2cos(2Pi-\frac{Pi}{3})=\\tg(Pi-\frac{Pi}{4})+2cos(Pi+\frac{2Pi}{3})=\\tg(-\frac{Pi}{4})+2cos(-\frac{Pi}{3})=\\=-tg(\frac{Pi}{4})+2cos(\frac{Pi}{3})=-1+2*(1/2)=0](https://tex.z-dn.net/?f=tg%28%5Cfrac%7B3Pi%7D%7B4%7D%29%2B2cos%28%5Cfrac%7B5Pi%7D%7B3%7D%29%3D%5C%5Ctg%28Pi-%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%282Pi-%5Cfrac%7BPi%7D%7B3%7D%29%3D%5C%5Ctg%28Pi-%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%28Pi%2B%5Cfrac%7B2Pi%7D%7B3%7D%29%3D%5C%5Ctg%28-%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%28-%5Cfrac%7BPi%7D%7B3%7D%29%3D%5C%5C%3D-tg%28%5Cfrac%7BPi%7D%7B4%7D%29%2B2cos%28%5Cfrac%7BPi%7D%7B3%7D%29%3D-1%2B2%2A%281%2F2%29%3D0)
<span>4sin7pi/6+ctg5pi/4=</span>
<span>![4sin(7pi/6)+ctg(5pi/4)=\\4sin(Pi+(pi/6))+ctg(Pi+(5pi/4))=\\4*(-sin(pi/6))+ctg(pi/4)=\\4*(-1/2)+1=\\=-2+1=-1](https://tex.z-dn.net/?f=4sin%287pi%2F6%29%2Bctg%285pi%2F4%29%3D%5C%5C4sin%28Pi%2B%28pi%2F6%29%29%2Bctg%28Pi%2B%285pi%2F4%29%29%3D%5C%5C4%2A%28-sin%28pi%2F6%29%29%2Bctg%28pi%2F4%29%3D%5C%5C4%2A%28-1%2F2%29%2B1%3D%5C%5C%3D-2%2B1%3D-1)
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2cos^2a-cos2a=
![2cos^2a-cos2a=\\2cos^2a-(cos^2a-sin^2a)=\\2cos^2a-(cos^2a-(1-cos^2a))=\\2cos^2a-(2cos^2a-1)=\\2cos^2a-2cos^2a+1=1](https://tex.z-dn.net/?f=2cos%5E2a-cos2a%3D%5C%5C2cos%5E2a-%28cos%5E2a-sin%5E2a%29%3D%5C%5C2cos%5E2a-%28cos%5E2a-%281-cos%5E2a%29%29%3D%5C%5C2cos%5E2a-%282cos%5E2a-1%29%3D%5C%5C2cos%5E2a-2cos%5E2a%2B1%3D1)
4sina*cosa*cos2a=
![4sina*cosa*cos2a=\\2*(2sina*cosa)*cos2a=\\2sin2a*cos2a=sin4a](https://tex.z-dn.net/?f=4sina%2Acosa%2Acos2a%3D%5C%5C2%2A%282sina%2Acosa%29%2Acos2a%3D%5C%5C2sin2a%2Acos2a%3Dsin4a)
найдите cos2a,если sina=1/корень из 3
![sina=1/\sqrt{3}\ => cos2a=1-2sin^2a=\\1-(1/\sqrt{3})^2=\\1-1/3=2/3](https://tex.z-dn.net/?f=sina%3D1%2F%5Csqrt%7B3%7D%5C+%3D%3E+cos2a%3D1-2sin%5E2a%3D%5C%5C1-%281%2F%5Csqrt%7B3%7D%29%5E2%3D%5C%5C1-1%2F3%3D2%2F3)
найдите sin2a,если cosa=-1/корень из 5 и pi/2
![sin2a,cosa=-1/\sqrt{5},\\Pi/2<a<pi\=,Pi<2a<2Pi=>sin2a<0\\sin2a=2sina*cosa=\\2*\sqrt{1-cos^2a}*cosa=\\2*\sqrt{1-1/5}*(-1/\sqrt{5})=-(2/\sqrt{5}*2/\sqrt{5})=\\=-2/5](https://tex.z-dn.net/?f=sin2a%2Ccosa%3D-1%2F%5Csqrt%7B5%7D%2C%5C%5CPi%2F2%3Ca%3Cpi%5C%3D%2CPi%3C2a%3C2Pi%3D%3Esin2a%3C0%5C%5Csin2a%3D2sina%2Acosa%3D%5C%5C2%2A%5Csqrt%7B1-cos%5E2a%7D%2Acosa%3D%5C%5C2%2A%5Csqrt%7B1-1%2F5%7D%2A%28-1%2F%5Csqrt%7B5%7D%29%3D-%282%2F%5Csqrt%7B5%7D%2A2%2F%5Csqrt%7B5%7D%29%3D%5C%5C%3D-2%2F5)
(1,8 - 0,3*у)*(2*у+9) = 0
Раскрываем скобки
3,6*у + 16,2 - 0,6*у² - 2,7*у = 0
Приводим подобные члены
-0,6*у² +0,9*у + 16,2 = 0 - квадратное уравнение.
Находим дискриминант - D= 39,69 и √39,69 =6,3 и
корни х1= - 4,5 х2 = 6 - ОТВЕТ
1) 3/√5
3√5/√5√5
3√5/5
2) 2/√6
2√6/√6√6
2√6/6
√6/3
3) 1/2-√3
1(2+√3)/(2-√3)(2+√3)
2+√3/4-3
2+√3/4-3
2+√3/1
2+√3
4) 1/3+√2
1(3-√2)/(3+√2)(3-√2)
3-√2/9-2
3-√2/7
5) 4/√7-√3
4(√7+√3)/(√7-√3)(√7+√3)
4(√7+√3)/4
√7+√3
6) 3/√5+√2
3(√5-√2)/(√5+√2)(√5-√2)
3(√5-√2)/5-2
3(√5-√2)/3
√5-√2
7) √5-√7/√5+√7
(√5-√7)(√5-√7)/(√5+√7)(√5-√7)
(√5-√7)^2/5-7
5-2√35+7/-2
2(6-√35)/-2
-(6-√35)
-6+√35
8) √10+√8/√10-√8
√10+2√2/√10-2√2
(√10+2√2)(√10+2√2)/(√10-2√2)(√10+2√2)
(√10+2√2)2/10-4*2
10+4√20+8/10-8
10+8√5+8/2
18+8√5/2
2(9+4√5)/2
9+4√5
я решала это так
1)раскрывала дробь
2)вычисляла произведения