1) sin(2π-x)=1
2π-x=π/2 +2k,k∈Z
-x=π/2 -2π+2πk,kZ
x=3π/2 -2πk,k∈Z
Ответ: x=3π/2 -2πk,k∈Z
2) cos4x=0.5
cos4x=1/2
4x=+-arccos1/2 +2πk,k∈Z
4x=+-π/3 +2πk,k∈Z
x=+-π/12 +πk/2,k∈Z
Ответ: x=+-π/12 +πk/2,k∈Z
3) tg(x-4π)=1
x-4π=π/4 +πk,k∈Z
x=π/4 +4π+πk,k∈Z
x=17π/4 +πk,k∈Z
Ответ: x=17π/4 +πk,k∈Z
Xy =x+y +19999 ;
(x-1)(y -1) =19999 +1 ;
(x-1)(y -1) =20000 ;
(x-1)(y -1) =5⁴*2⁵ ;
* * * (4+1)(5+1) =5*6 =30 делителей * * *
ответ : 15 пар.