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Ответ:

1. arcsin (- 1/2) = - arcsin 1/2 = - π/6

  arccos √3/2 = π/6

  - π/6 < π/6,  ⇒  

  arcsin (- 1/2) <  arccos √3/2

2. arccos 1/2 = π/3

   arcsin √3/2 = π/3

   arccos 1/2 = arcsin √3/2

3. arcctg √3 = π/6

   arcsin 1 = π/2

   π/6 < π/2,   ⇒

  arcctg √3 < arcsin 1

4. arccos (- 1/2) = π - arccos 1/2 = π - π/3 = 2π/3

   arcctg 1 = π/4

   2π/3 > π/4,   ⇒

   arccos (- 1/2) > arcctg 1