Для начала найдем значение углов:

3π/2 + a = 3π/2 + 5π/12 = 18π/12 + 5π/12 = 23π/12
π - a = π - 5π/12 = 12π/12 - 5π/12 = 7π/12

Теперь найдем значение sin^2(23π/12) и sin^2(7π/12):

sin^2(23π/12) = sin^2(2π + 11π/12) = sin^2(11π/12) = (sin(11π/12))^2
sin(11π/12) = -sin(π - 11π/12) = -sin(π/12) = -(1/2)
(sin(11π/12))^2 = (-1/2)^2 = 1/4

sin^2(7π/12) = sin^2(π - 5π/12) = sin^2(5π/12) = (sin(π/12))^2
sin(5π/12) = sin(π - 7π/12) = sin(π/12) = 1/2
(sin(π/12))^2 = (1/2)^2 = 1/4

Теперь найдем искомое значение:

sin^2(23π/12) - sin^2(7π/12) = 1/4 - 1/4 = 0

Итак, значение выражения sin^2(3π/2 + a) - sin^2(π - a) при a = 5π/12 равно 0.