Evaluate: $2\sin^2 30° \cdot \sec 60° + \tan^2 60°$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
Using standard values: $\sin 30° = \dfrac{1}{2}$, $\sec 60° = 2$, $\tan 60° = \sqrt{3}$
$$2\sin^2 30° \cdot \sec 60° + \tan^2 60°$$
$$= 2 \times \left(\frac{1}{2}\right)^2 \times 2 + (\sqrt{3})^2$$
$$= 2 \times \frac{1}{4} \times 2 + 3$$
$$= 1 + 3 = \boxed{4}$$
Source: Chapter 8, Section 8.3 (Table 8.1)
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Explanation
- Write the values first — examiners award a step mark for correctly substituting standard ratios from Table 8.1.
- Show each arithmetic step to earn the process mark; don't jump straight to the answer.
- Common error: forgetting to square $\sin 30°$ before multiplying, or confusing $\sec 60° = 2$ with $\cos 60° = \frac{1}{2}$.