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1. $\sin30^{\circ}\cos45^{\circ}-\tan60^{\circ}+3\tan30^{\circ}$.
答案：
1. 解:原式$=\frac{1}{2} × \frac{\sqrt{2}}{2} - \sqrt{3} + 3 × \frac{\sqrt{3}}{3} = \frac{\sqrt{2}}{4} - \sqrt{3} + \sqrt{3} = \frac{\sqrt{2}}{4}$
2. $4\sin^{2}30^{\circ}+\tan60^{\circ}-2\cos30^{\circ}$.
答案：
2. 解:原式$=4 × (\frac{1}{2})^2 + \sqrt{3} - 2 × \frac{\sqrt{3}}{2} = 1 + \sqrt{3} - \sqrt{3} = 1.$
3. $2\sin60^{\circ}·\tan30^{\circ}+\cos^{2}30^{\circ}-\tan45^{\circ}$.
答案：
3. 解:原式$=2 × \frac{\sqrt{3}}{2} × \frac{\sqrt{3}}{3} + (\frac{\sqrt{3}}{2})^2 - 1 = 1 + \frac{3}{4} - 1 = \frac{3}{4}.$
4. $\tan45^{\circ}\sin45^{\circ}+\cos^{2}30^{\circ}$.
答案：
4. 解:原式$=1 × \frac{\sqrt{2}}{2} + (\frac{\sqrt{3}}{2})^2 = \frac{\sqrt{2}}{2} + \frac{3}{4} = \frac{2\sqrt{2} + 3}{4}$
5. $4\cos30^{\circ}+\tan^{2}45^{\circ}-2\tan60^{\circ}$.
答案：
5. 解:原式$=4 × \frac{\sqrt{3}}{2} + 1^2 - 2 × \sqrt{3} = 2\sqrt{3} + 1 - 2\sqrt{3} = 1.$
6. $\tan30^{\circ}\sin60^{\circ}-\cos45^{\circ}\sin45^{\circ}$.
答案：
6. 解:原式$=\frac{\sqrt{3}}{3} × \frac{\sqrt{3}}{2} - \frac{\sqrt{2}}{2} × \frac{\sqrt{2}}{2} = \frac{1}{2} - \frac{1}{2} = 0.$
7. $8\sin^{2}60^{\circ}+\tan45^{\circ}-4\cos30^{\circ}$.
答案：
7. 解:原式$=8 × (\frac{\sqrt{3}}{2})^2 + 1 - 4 × \frac{\sqrt{3}}{2} = 8 × \frac{3}{4} + 1 - 2\sqrt{3} = 6 + 1 - 2\sqrt{3} = 7 - 2\sqrt{3}.$
8. $2\cos^{2}45^{\circ}+\tan60^{\circ}·\tan30^{\circ}-\cos60^{\circ}$.
答案：
8. 解:原式$=2 × (\frac{\sqrt{2}}{2})^2 + \sqrt{3} × \frac{\sqrt{3}}{3} - \frac{1}{2} = 1 + 1 - \frac{1}{2} = \frac{3}{2}.$
9. $4\sin60^{\circ}-3\tan30^{\circ}+2\cos45^{\circ}$.
答案：
9. 解:原式$=4 × \frac{\sqrt{3}}{2} - 3 × \frac{\sqrt{3}}{3} + 2 × \frac{\sqrt{2}}{2} = 2\sqrt{3} - \sqrt{3} + \sqrt{2} = \sqrt{3} + \sqrt{2}.$
10. $2\tan60^{\circ}\cos30^{\circ}-\sin^{2}45^{\circ}$.
答案：
10. 解:原式$=2 × \sqrt{3} × \frac{\sqrt{3}}{2} - (\frac{\sqrt{2}}{2})^2 = 3 - \frac{1}{2} = \frac{5}{2}.$
11. $3\tan30^{\circ}+\cos^{2}30^{\circ}-2\sin60^{\circ}$.
答案：
11. 解:原式$=3 × \frac{\sqrt{3}}{3} + (\frac{\sqrt{3}}{2})^2 - 2 × \frac{\sqrt{3}}{2} = \sqrt{3} + \frac{3}{4} - \sqrt{3} = \frac{3}{4}.$
12. $3\tan30^{\circ}-\tan^{2}45^{\circ}+2\sin60^{\circ}$.
答案：
12. 解:原式$=3 × \frac{\sqrt{3}}{3} - 1 + 2 × \frac{\sqrt{3}}{2} = \sqrt{3} - 1 + \sqrt{3} = 2\sqrt{3} - 1.$
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