Верно ли равенство: a) sin(7π/12) - sin(π/12) = √2/2 б) cos(11π/24) - cos(π/8) = -sin(π/6)

a) sin(7π/12) - sin(π/12) = √2/2 Используем формулу разности синусов: sin(x) - sin(y) = 2 * cos((x+y)/2) * sin((x-y)/2) sin(7π/12) - sin(π/12) = 2 * cos((7π/12 + π/12)/2) * sin((7π/12 - π/12)/2) = 2 * cos(8π/24) * sin(6π/24) = 2 * cos(π/3) * sin(π/4) = 2 * (1/2) * (√2/2) = √2/2. Равенство верно. б) cos(11π/24) - cos(π/8) = -sin(π/6) Используем формулу разности косинусов: cos(x) - cos(y) = -2 * sin((x+y)/2) * sin((x-y)/2) cos(11π/24) - cos(3π/24) = -2 * sin((11π/24 + 3π/24)/2) * sin((11π/24 - 3π/24)/2) = -2 * sin((14π/24)/2) * sin((8π/24)/2) = -2 * sin(7π/24) * sin(π/6) = -2 * sin(7π/24) * (1/2) = -sin(7π/24) -sin(7π/24) ≠ -sin(π/6), равенство неверно.