1. Вычислите: a) 2 arcsin(sqrt(2)/2) - 1/2 arctg(sqrt(3)); б) ctg (arccos(1/2) + arcsin(sqrt(3)/2)).

a) 2 * (π/4) - 1/2 * (π/3) = π/2 - π/6 = 3π/6 - π/6 = 2π/6 = π/3.
б) arccos(1/2) = π/3, arcsin(sqrt(3)/2) = π/3. ctg(π/3 + π/3) = ctg(2π/3) = -1/sqrt(3) = -sqrt(3)/3.