Generated by claude-sonnet-4-6 · 2026-06-15 10:27 · grounding rag
Model Answer
Substituting standard values: $\cos 45° = \dfrac{1}{\sqrt{2}}$, $\sin 30° = \dfrac{1}{2}$, $\cos 30° = \dfrac{\sqrt{3}}{2}$
$$2\sqrt{2}\cos 45°\sin 30° + 2\sqrt{3}\cos 30°$$
$$= 2\sqrt{2} \times \frac{1}{\sqrt{2}} \times \frac{1}{2} + 2\sqrt{3} \times \frac{\sqrt{3}}{2}$$
$$= 2\sqrt{2} \times \frac{1}{2\sqrt{2}} + 2\sqrt{3} \times \frac{\sqrt{3}}{2}$$
$$= 1 + 3 = \boxed{4}$$
Source: Chapter 8, Section 8.3 (Table 8.1)
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Explanation
- Examiner expects you to write down the values used, substitute clearly, and simplify step by step — each step can earn partial marks.
- Key values to remember: $\cos 45°=\frac{1}{\sqrt{2}}$, $\sin 30°=\frac{1}{2}$, $\cos 30°=\frac{\sqrt{3}}{2}$.
- Notice $2\sqrt{2} \times \frac{1}{\sqrt{2}} = 2$ and $2\sqrt{3} \times \frac{\sqrt{3}}{2} = 3$, giving a clean integer answer 4. Always simplify surds fully.