Найдите числовое значение выражения: a) 8 sin(π/6) cos(2π/3) tg(4π/3) ctg(7π/4) б) 10 ctg(3π/4) sin(5π/4) cos(7π/4)

a) 8 sin(π/6) cos(2π/3) tg(4π/3) ctg(7π/4) sin(π/6) = 1/2 cos(2π/3) = -1/2 tg(4π/3) = tg(π + π/3) = tg(π/3) = √3 ctg(7π/4) = ctg(2π - π/4) = ctg(-π/4) = -1 8 * (1/2) * (-1/2) * √3 * (-1) = 8 * (1/4) * √3 = 2√3 б) 10 ctg(3π/4) sin(5π/4) cos(7π/4) ctg(3π/4) = ctg(π - π/4) = -ctg(π/4) = -1 sin(5π/4) = sin(π + π/4) = -sin(π/4) = -√2/2 cos(7π/4) = cos(2π - π/4) = cos(-π/4) = cos(π/4) = √2/2 10 * (-1) * (-√2/2) * (√2/2) = 10 * (√2/2) * (√2/2) = 10 * (2/4) = 10 * (1/2) = 5