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 используем свойства четности и нечетности тригонометрических функций: $\cos(-x) = \cos x$, а $\sin(-x) = -\sin x$, $\text{tg}(-x) = -\text{tg } x$, $\text{ctg}(-x) = -\text{ctg } x$. 1) $\cos\left(-\frac{\pi}{6}\right) \sin\left(-\frac{\pi}{3}\right) + \text{tg}\left(-\frac{\pi}{4}\right) = \cos\frac{\pi}{6} \cdot \left(-\sin\frac{\pi}{3}\right) - \text{tg}\frac{\pi}{4} = \frac{\sqrt{3}}{2} \cdot \left(-\frac{\sqrt{3}}{2}\right) - 1 = -\frac{3}{4} - 1 = -1,75$ 2) $\frac{1 + \text{tg}^2\left(-\frac{\pi}{6}\right)}{1 + \text{ctg}^2\left(-\frac{\pi}{6}\right)} = \frac{1 + \left(-\frac{1}{\sqrt{3}}\right)^2}{1 + (-\sqrt{3})^2} = \frac{1 + \frac{1}{3}}{1 + 3} = \frac{\frac{4}{3}}{4} = \frac{1}{3}$ 3) $2\sin\left(-\frac{\pi}{6}\right)\cos\left(-\frac{\pi}{6}\right) + \text{tg}\left(-\frac{\pi}{3}\right) + \sin^2\left(-\frac{\pi}{4}\right) = 2\cdot\left(-\frac{1}{2}\right)\cdot\frac{\sqrt{3}}{2} - \sqrt{3} + \left(-\frac{\sqrt{2}}{2}\right)^2 = -\frac{\sqrt{3}}{2} - \sqrt{3} + \frac{1}{2} = 0,5 - 1,5\sqrt{3}$ 4) $\cos(-\pi) + \text{ctg}\left(-\frac{\pi}{2}\right) - \sin\left(-\frac{3}{2}\pi\right) + \text{ctg}\left(-\frac{\pi}{4}\right) = \cos\pi - \text{ctg}\frac{\pi}{2} + \sin\frac{3}{2}\pi - \text{ctg}\frac{\pi}{4} = -1 - 0 + (-1) - 1 = -3$ 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) $2\sin\left(-\frac{\pi}{6}\right) + 3 + 7,5\text{tg}(-\pi) + \frac{1}{8}\cos\frac{3}{2}\pi = 2\cdot\left(-\frac{1}{2}\right) + 3 - 7,5\cdot 0 + \frac{1}{8}\cdot 0 = -1 + 3 = 2$ **Ответ: 1) -1,75; 2) 1/3; 3) 0,5 - 1,5√3; 4) -3; 5) √2; 6) 2.**