Generated by claude-sonnet-4-6 · 2026-06-15 10:22 · grounding rag
Model Answer
Using standard values: $\sin 30° = \dfrac{1}{2}$, $\cos 60° = \dfrac{1}{2}$, $\tan 45° = 1$
$$\frac{\sin^2 30° + \cos^2 60°}{1 + \tan^2 45°} = \frac{\left(\dfrac{1}{2}\right)^2 + \left(\dfrac{1}{2}\right)^2}{1 + (1)^2}$$
$$= \frac{\dfrac{1}{4} + \dfrac{1}{4}}{1 + 1} = \frac{\dfrac{1}{2}}{2} = \boxed{\dfrac{1}{4}}$$
Source: Chapter 8, Section 8.3 (Table 8.1)
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Explanation
- Examiners expect you to first state the values substituted, then show step-by-step simplification.
- $\sin 30° = \cos 60° = \frac{1}{2}$ and $\tan 45° = 1$ are standard values from Table 8.1 — memorise the full table.
- A common mistake is forgetting to square the values before adding. Write each step clearly to earn both marks.