№2. Вычислите: 1) 2 sin 30° - tg 45° + ctg 30° 2) √3 sin(π/3) - 2 cos(π/6) + (√3/2)tg(π/3) 3) sin(-π/6)cos(-π/4) - sin(-π/4)cos(-π/6)

1) 2 sin 30° - tg 45° + ctg 30° = 2 * (1/2) - 1 + √3 = 1 - 1 + √3 = √3. 2) √3 sin(π/3) - 2 cos(π/6) + (√3/2)tg(π/3) = √3 * (√3/2) - 2 * (√3/2) + (√3/2) * √3 = 3/2 - √3 + 3/2 = 3 - √3. 3) sin(-π/6)cos(-π/4) - sin(-π/4)cos(-π/6) = sin(-π/6 - (-π/4)) = sin(-π/6 + π/4) = sin(π/12). Или: sin(-π/6) = -1/2, cos(-π/4) = √2/2 sin(-π/4) = -√2/2, cos(-π/6) = √3/2 (-1/2)(√2/2) - (-√2/2)(√3/2) = -√2/4 + √6/4 = (√6 - √2)/4 Формула для синуса разности углов: sin(a - b) = sin(a)cos(b) - cos(a)sin(b) sin(-π/6)cos(-π/4) - cos(-π/6)sin(-π/4) = sin(-π/6 - (-π/4)) = sin(π/12). sin(π/12) = (√6 - √2)/4.