**Ответ:**
1) $$\sqrt{2} \sin \frac{7\pi}{8} \cos \frac{7\pi}{8} = \frac{\sqrt{2}}{2} \sin \frac{7\pi}{4} = \frac{\sqrt{2}}{2} \cdot \left(-\frac{\sqrt{2}}{2}\right) = -\frac{2}{4} = -0,5$$
2) $$7\sqrt{2} \sin \frac{15\pi}{8} \cos \frac{15\pi}{8} = \frac{7\sqrt{2}}{2} \sin \frac{15\pi}{4} = \frac{7\sqrt{2}}{2} \cdot \left(-\frac{\sqrt{2}}{2}\right) = -\frac{7 \cdot 2}{4} = -3,5$$
3) $$10\sqrt{3} \sin \frac{7\pi}{6} \cos \frac{7\pi}{6} = 5\sqrt{3} \sin \frac{7\pi}{3} = 5\sqrt{3} \cdot \frac{\sqrt{3}}{2} = \frac{5 \cdot 3}{2} = 7,5$$
4) $$6\sqrt{3} \sin \frac{5\pi}{6} \cos \frac{5\pi}{6} = 3\sqrt{3} \sin \frac{5\pi}{3} = 3\sqrt{3} \cdot \left(-\frac{\sqrt{3}}{2}\right) = -\frac{3 \cdot 3}{2} = -4,5$$
5) $$3\sqrt{2} \cos^2 \frac{9\pi}{8} - 3\sqrt{2} \sin^2 \frac{9\pi}{8} = 3\sqrt{2} \cos \frac{9\pi}{4} = 3\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 3$$
6) $$4\sqrt{3} \cos^2 \frac{7\pi}{12} - 4\sqrt{3} \sin^2 \frac{7\pi}{12} = 4\sqrt{3} \cos \frac{7\pi}{6} = 4\sqrt{3} \cdot \left(-\frac{\sqrt{3}}{2}\right) = -6$$
7) $$\sqrt{18} \cos^2 \frac{7\pi}{8} - \sqrt{18} \sin^2 \frac{7\pi}{8} = 3\sqrt{2} \cos \frac{7\pi}{4} = 3\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 3$$
8) $$\sqrt{72} \cos^2 \frac{9\pi}{8} - \sqrt{72} \sin^2 \frac{9\pi}{8} = 6\sqrt{2} \cos \frac{9\pi}{4} = 6\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 6$$
9) $$\sqrt{32} \cos^2 \frac{7\pi}{8} - \sqrt{8} = 4\sqrt{2} \cos^2 \frac{7\pi}{8} - 2\sqrt{2} = 2\sqrt{2}(2\cos^2 \frac{7\pi}{8} - 1) = 2\sqrt{2} \cos \frac{7\pi}{4} = 2\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 2$$
10) $$2\sqrt{3} \cos^2 \frac{13\pi}{12} - \sqrt{3} = \sqrt{3}(2\cos^2 \frac{13\pi}{12} - 1) = \sqrt{3} \cos \frac{13\pi}{6} = \sqrt{3} \cdot \frac{\sqrt{3}}{2} = 1,5$$
11) $$\sqrt{108} \cos^2 \frac{7\pi}{12} - \sqrt{27} = 6\sqrt{3} \cos^2 \frac{7\pi}{12} - 3\sqrt{3} = 3\sqrt{3}(2\cos^2 \frac{7\pi}{12} - 1) = 3\sqrt{3} \cos \frac{7\pi}{6} = 3\sqrt{3} \cdot \left(-\frac{\sqrt{3}}{2}\right) = -4,5$$
12) $$\sqrt{128} \cos^2 \frac{7\pi}{8} - \sqrt{32} = 8\sqrt{2} \cos^2 \frac{7\pi}{8} - 4\sqrt{2} = 4\sqrt{2}(2\cos^2 \frac{7\pi}{8} - 1) = 4\sqrt{2} \cos \frac{7\pi}{4} = 4\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 4$$
13) $$\sqrt{2} - 2\sqrt{2} \sin^2 \frac{15\pi}{8} = \sqrt{2}(1 - 2\sin^2 \frac{15\pi}{8}) = \sqrt{2} \cos \frac{15\pi}{4} = \sqrt{2} \cdot \frac{\sqrt{2}}{2} = 1$$
14) $$5\sqrt{3} - 10\sqrt{3} \sin^2 \frac{13\pi}{12} = 5\sqrt{3}(1 - 2\sin^2 \frac{13\pi}{12}) = 5\sqrt{3} \cos \frac{13\pi}{6} = 5\sqrt{3} \cdot \frac{\sqrt{3}}{2} = 7,5$$
15) $$\sqrt{32} - \sqrt{128} \sin^2 \frac{9\pi}{8} = 4\sqrt{2} - 8\sqrt{2} \sin^2 \frac{9\pi}{8} = 4\sqrt{2}(1 - 2\sin^2 \frac{9\pi}{8}) = 4\sqrt{2} \cos \frac{9\pi}{4} = 4\sqrt{2} \cdot \frac{\sqrt{2}}{2} = 4$$
16) $$\sqrt{27} - \sqrt{108} \sin^2 \frac{11\pi}{12} = 3\sqrt{3} - 6\sqrt{3} \sin^2 \frac{11\pi}{12} = 3\sqrt{3}(1 - 2\sin^2 \frac{11\pi}{12}) = 3\sqrt{3} \cos \frac{11\pi}{6} = 3\sqrt{3} \cdot \frac{\sqrt{3}}{2} = 4,5$$
17) $$26\sqrt{2} \cos \frac{\pi}{4} \cos \frac{4\pi}{3} = 26\sqrt{2} \cdot \frac{\sqrt{2}}{2} \cdot \left(-\frac{1}{2}\right) = 26 \cdot \frac{1}{2} \cdot \left(-\frac{1}{2}\right) = -13/2 = -6,5$$
18) $$28\sqrt{2} \cos \frac{3\pi}{4} \cos \frac{7\pi}{3} = 28\sqrt{2} \cdot \left(-\frac{\sqrt{2}}{2}\right) \cdot \frac{1}{2} = -28 \cdot \frac{1}{2} \cdot \frac{1}{2} = -7$$
19) $$18\sqrt{2} \text{tg} \frac{\pi}{4} \sin \frac{3\pi}{4} = 18\sqrt{2} \cdot 1 \cdot \frac{\sqrt{2}}{2} = 18$$
20) $$12\sqrt{2} \text{tg} \frac{5\pi}{4} \sin \frac{3\pi}{4} = 12\sqrt{2} \cdot 1 \cdot \frac{\sqrt{2}}{2} = 12$$
21) $$12 \sin 150^\circ \cos 120^\circ = 12 \cdot \frac{1}{2} \cdot \left(-\frac{1}{2}\right) = -3$$
22) $$14 \sin 45^\circ \cos 135^\circ = 14 \cdot \frac{\sqrt{2}}{2} \cdot \left(-\frac{\sqrt{2}}{2}\right) = -7$$
23) $$12\sqrt{2} \cos(-225^\circ) = 12\sqrt{2} \cos(225^\circ) = 12\sqrt{2} \cdot \left(-\frac{\sqrt{2}}{2}\right) = -12$$
24) $$4\sqrt{3} \sin(-120^\circ) = -4\sqrt{3} \sin(120^\circ) = -4\sqrt{3} \cdot \frac{\sqrt{3}}{2} = -6$$
