Решение:

1. $$cos^2 45° + tg^2 60° = (\frac{\sqrt{2}}{2})^2 + (\sqrt{3})^2 = \frac{2}{4} + 3 = \frac{1}{2} + 3 = 3\frac{1}{2} = 3.5$$
2. $$2cos^2 60° - sin^2 30° + sin 60° \cdot ctg 60° = 2 \cdot (\frac{1}{2})^2 - (\frac{1}{2})^2 + \frac{\sqrt{3}}{2} \cdot \frac{\sqrt{3}}{3} = 2 \cdot \frac{1}{4} - \frac{1}{4} + \frac{3}{2 \cdot 3} = \frac{1}{2} - \frac{1}{4} + \frac{1}{2} = \frac{2-1+2}{4} = \frac{3}{4} = 0.75$$

Ответ: 1) $$3.5$$, 2) $$0.75$$