438 Найти значение выражения: 1) sin pi/4 cos pi/4 - sin pi/3 cos pi/6; 2) 2 tg^2 pi/3 - ctg^2 pi/6 - sin pi/6 cos pi/3; 3) (tg pi/4 - ctg pi/3)(ctg pi/4 + tg pi/6); 4) 2 cos^2 pi/6 - sin^2 pi/3 + tg pi/6 ctg pi/3.

1) $\sin \frac{\pi}{4} \cos \frac{\pi}{4} - \sin \frac{\pi}{3} \cos \frac{\pi}{6} = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{2}}{2} - \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{2} = \frac{2}{4} - \frac{3}{4} = -\frac{1}{4} = -0,25$ 2) $2 \tan^2 \frac{\pi}{3} - \cot^2 \frac{\pi}{6} - \sin \frac{\pi}{6} \cos \frac{\pi}{3} = 2 \cdot (\sqrt{3})^2 - (\sqrt{3})^2 - \frac{1}{2} \cdot \frac{1}{2} = 2 \cdot 3 - 3 - \frac{1}{4} = 6 - 3 - 0,25 = 2,75$ 3) $(\tan \frac{\pi}{4} - \cot \frac{\pi}{3})(\cot \frac{\pi}{4} + \tan \frac{\pi}{6}) = (1 - \frac{\sqrt{3}}{3})(1 + \frac{\sqrt{3}}{3}) = 1^2 - (\frac{\sqrt{3}}{3})^2 = 1 - \frac{3}{9} = 1 - \frac{1}{3} = \frac{2}{3}$ 4) $2 \cos^2 \frac{\pi}{6} - \sin^2 \frac{\pi}{3} + \tan \frac{\pi}{6} \cot \frac{\pi}{3} = 2 \cdot (\frac{\sqrt{3}}{2})^2 - (\frac{\sqrt{3}}{2})^2 + \frac{\sqrt{3}}{3} \cdot \frac{\sqrt{3}}{3} = 2 \cdot \frac{3}{4} - \frac{3}{4} + \frac{3}{9} = \frac{6}{4} - \frac{3}{4} + \frac{1}{3} = \frac{3}{4} + \frac{1}{3} = \frac{9}{12} + \frac{4}{12} = \frac{13}{12} = 1\frac{1}{12}$