Вычислить: 1) cos(-π/6)sin(-π/3) + tg(-π/4); 2) (1+tg²(-π/6))/(1+ctg²(-π/6)); 3) 2sin(-π/6)cos(-π/6) + tg(-π/3) + sin²(-π/4); 4) cos(-π) + ctg(-π/2) - sin(-3π/2) + ctg(-π/4); 5) (3-sin²(-π/3)-cos²(-π/3))/(2cos(-π/4)); 6) 2sin(-π/6) + 3 + 7,5tg(-π) + 1/8cos(3π/2)

Для решения воспользуемся свойствами чётности функций ($\\cos(-x) = \\cos x$, а для остальных функций $\\sin, \\tg, \\ctg$ знак «минус» выносится вперед) и табличными значениями. 1) $\\cos \\left(-\\frac{\\pi}{6}\\right) \\sin \\left(-\\frac{\\pi}{3}\\right) + \\tg \\left(-\\frac{\\pi}{4}\\right) = \\cos \\frac{\\pi}{6} \\cdot \\left(-\\sin \\frac{\\pi}{3}\\right) - \\tg \\frac{\\pi}{4} = \\frac{\\sqrt{3}}{2} \\cdot \\left(-\\frac{\\sqrt{3}}{2}\\right) - 1 = -\\frac{3}{4} - 1 = -1\\frac{3}{4} = -1,75$ 2) $\\frac{1 + \\tg^2 \\left(-\\frac{\\pi}{6}\\right)}{1 + \\ctg^2 \\left(-\\frac{\\pi}{6}\\right)} = \\frac{1 + \\left(-\\frac{1}{\\sqrt{3}}\\right)^2}{1 + (-\\sqrt{3})^2} = \\frac{1 + \\frac{1}{3}}{1 + 3} = \\frac{4/3}{4} = \\frac{4}{3} \\cdot \\frac{1}{4} = \\frac{1}{3}$ 3) $2 \\sin \\left(-\\frac{\\pi}{6}\\right) \\cos \\left(-\\frac{\\pi}{6}\\right) + \\tg \\left(-\\frac{\\pi}{3}\\right) + \\sin^2 \\left(-\\frac{\\pi}{4}\\right) = 2 \\cdot \\left(-\\frac{1}{2}\\right) \\cdot \\frac{\\sqrt{3}}{2} - \\sqrt{3} + \\left(-\\frac{\\sqrt{2}}{2}\\right)^2 = -\\frac{\\sqrt{3}}{2} - \\sqrt{3} + \\frac{1}{2} = \\frac{1 - 3\\sqrt{3}}{2}$ 4) $\\cos(-\\pi) + \\ctg \\left(-\\frac{\\pi}{2}\\right) - \\sin \\left(-\\frac{3}{2}\\pi \\right) + \\ctg \\left(-\\frac{\\pi}{4}\\right) = -1 + 0 - (1) - 1 = -3$ 5) $\\frac{3 - \\sin^2 \\left(-\\frac{\\pi}{3}\\right) - \\cos^2 \\left(-\\frac{\\pi}{3}\\right)}{2 \\cos \\left(-\\frac{\\pi}{4}\\right)} = \\frac{3 - (\\sin^2 \\frac{\\pi}{3} + \\cos^2 \\frac{\\pi}{3})}{2 \\cos \\frac{\\pi}{4}} = \\frac{3 - 1}{2 \\cdot \\frac{\\sqrt{2}}{2}} = \\frac{2}{\\sqrt{2}} = \\sqrt{2}$ 6) $2 \\sin \\left(-\\frac{\\pi}{6}\\right) + 3 + 7,5 \\tg(-\\pi) + \\frac{1}{8} \\cos \\frac{3}{2}\\pi = 2 \\cdot \\left(-\\frac{1}{2}\\right) + 3 + 7,5 \\cdot 0 + \\frac{1}{8} \\cdot 0 = -1 + 3 = 2$ **Ответ: 1) -1,75; 2) 1/3; 3) (1 - 3√3)/2; 4) -3; 5) √2; 6) 2.**