1) arccos(-1) = π
arccos(1/2) = π/3
arccos(-√3/2) = 5π/6
Answer: π - π/3 - 3(5π/6)

2) 2cos(t) = 1
cos(t) = 1/2
Answer: t = π/3

3) -2cos(t) = 0
cos(t) = 0
Answer: t = π/2

4) cos(arcctg(√3))
arcctg(√3) = π/6
cos(π/6) = √3/2
Answer: √3/2

5) arcctg(ctg(2π/3))
ctg(2π/3) = -√3
arcctg(-√3) = -π/3
Answer: -π/3

6) ctg(x) = -0.5
x = arctan(-2)
x = -26.565° or -π/6

7) ctg(x) = 0
x = arctan(0)
x = 0