6.5

Решение:

а) arcctg 1 - arctg √3 - arccos(-1/2) = π/4 - π/3 - 2π/3 = 3π - 4π - 8π/12 = -9π/12 = -3π/4 = -135°

б) arcsin(-1/2) + arctg(-1/√3) - arcctg √3 = -π/6 - arctg 1/√3 - π/6 = -π/6 - arctg √3/3 - π/6 = -π/6 - π/6 - π/6 = -3π/6 = -π/2 = -90°

в) arcsin(-1) - 3/2 × arccos 1/2 + 3arcctg(-1/√3) = -π/2 - 3/2 × π/3 + 3(π-arcctg 1/√3) = -π/2 - π/2 + 3π - 3arcctg 1/√3 = -π/2 - π/2 + 3π - 3arcctg √3/3 = -π/2 - π/2 + 3π - 3×π/3 = -π/2 - π/2 + 3π - π = -π-π+6π-2π/2 = 2π/2 = π = 180°

г) -4arcsin(-√2/2) + 8arccos(-√2/2) - 15arcctg √3/3 = -4×(-π/4) + 8×3π/4 - 15×π/6 = 4×π/4 + 8×3π/4 - 15×π/6 = π + 2×3π - 5×π/2 = π + 6π - 5π/2 = 2π+12π-5π/2 = 9π/2 = 810°