16. cos²(2t + π/6) = 1/2

Ответ: t = π/24 + πn/2, t = -5π/24 + πn/2, n ∈ Z

Решаем уравнение cos²(2t + π/6) = 1/2:

Берем квадратный корень из обеих частей: cos(2t + π/6) = ±√(1/2) = ±√2 / 2

2t + π/6 = π/4 + πn, 2t + π/6 = -π/4 + πn

2t + π/6 = 3π/4 + πn, 2t + π/6 = -3π/4 + πn

2t = π/4 - π/6 + πn, 2t = -π/4 - π/6 + πn

2t = 3π/4 - π/6 + πn, 2t = -3π/4 - π/6 + πn

2t = π/12 + πn, 2t = -5π/12 + πn

2t = 7π/12 + πn, 2t = -11π/12 + πn

t = π/24 + πn/2, t = -5π/24 + πn/2

t = 7π/24 + πn/2, t = -11π/24 + πn/2

Ответ: t = π/24 + πn/2, t = -5π/24 + πn/2, t = 7π/24 + πn/2, t = -11π/24 + πn/2, n ∈ Z