Reading Task 1. Read the text about fast food.Fast foodHow did the hamburger become the most popular, most typical American food?It got its name from the German town of Hamburg, wluch was famous for its steak. Germanimmigrants to the United States introduced the hamburger steak“ McDonald's sells hamburgers, one of the world's most famous fast food restaurantsYou can find them in Japan, Germany. Panama, Guatemala, Australia, Portugal Hong Kongand even Moscow. In fact, there are 13, 000 in 120 countries.What makes American fast food so popular?Lee Cho, a South Korean, says: "I often go io McDonald's. It's clean, less expensive thanother re​

а) cos(2arcsin1/2),
arcsin1/2=п/6 cos(2*П/6)=cosП/3=1/2
б) tg(arcctg3)=1/ctg(arcctg(3))=1/3
в) ctg(2arcctg2)=(ctg^2(arcctg2)-1)/2ctg(arcctg2))=(4-1)/4=3/4
г) sin (arctg3)=3/sqrt(10)
tgx=3 sinx/cosx=3  sin^2x=9(1-sin^2x)  10sin^2x=9 sinx=3/sqrt(10)
8_ Решите уравнение
а) 2cos x +V3=0 
cosx=-sqrt(3)/2  cos(П+a)=-cosa
x=П+-П/6+2Пk
б) V3tg x  - 1=0
tgx=1/sqrt(3) x=П/3+Пk
в)6 sinx -5=0 sinx=5/6  x=(-1)^k*arcsin(5/6)+Пk
 г) 2 sin (2x+п/6)=V3
sin(2x+п/6)=sqrt(3)/2
2x+П/6=(-1)^k*П/3+Пk
x=(-1)^k*П/6-П/12+Пk/2
д)V3 ctg (x/2 - п/4)=1 
ctg(x/2-п/4)=1/sqrt(3)
x/2-п/4=П/6+Пk
x/2=П/6+П/4+Пk
x=П/3+п/2+2Пk=5П/6+2Пk
е) tg 3 x =9
3x=arctg9+Пk  x=1/3arctg9+Пk/3
а) sinx < или равно V3/2
-4/3П+2пk<=x<=П/3+2Пk
б) cosx+0.5<0
cosx<-1/2 
П/2+П/6+2Пk<x<3/2П-П/6+2Пk
2П/3+2Пk<x<4П/3+2Пk
 в) 3 tgx-V3>0
tgx>sqrt(3)/3
П/3+Пk<x<П/2+Пk
 г)V2 sin (п/3+x/2)>1
sin(П/3+x/2)>sqrt(2)/2  П/3+x/2=t
sint>sqrt(2)/2
П/4+2Пk<t<3П/4+2Пk
П/4+2Пk<П/3+x/2<3П/4+2Пk
-П/6+4Пk<x<5П/6+4Пk
д) 2cosx> или равно  -V2
cosx>=-sqrt(2)/2
-3П/4+2Пk<x>3П/4+2Пk
е) V3tg (3x+ п/6)<1
tg(3x+П/6)<sqrt(3)/3  t=3x+П/6  tgt<sqrt(3)/3
-П/2+Пk<t<П/3+Пk
-П/2+пk<3x+П/6<п/3+Пk
-2П/3+Пk<3x<П/6+Пk
-2П/9+Пk/3<x<П/18+Пk/3