If $x\cos 60° + y\cos 0° + \sin 30° - \cot 45° = 5$, then find the value of $x + 2y$.
Generated by claude-sonnet-4-6 · 2026-06-15 10:21 · grounding rag
Model Answer
Substituting standard values: $\cos 60° = \dfrac{1}{2}$, $\cos 0° = 1$, $\sin 30° = \dfrac{1}{2}$, $\cot 45° = 1$
$$x \cdot \frac{1}{2} + y \cdot 1 + \frac{1}{2} - 1 = 5$$
$$\frac{x}{2} + y - \frac{1}{2} = 5$$
$$\frac{x}{2} + y = 5 + \frac{1}{2} = \frac{11}{2}$$
Multiplying both sides by 2:
$$x + 2y = 11$$
Source: Chapter 8, Section 8.3 (Table 8.1)
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Explanation
- Substitute exact values from Table 8.1: cos 60° = ½, cos 0° = 1, sin 30° = ½, cot 45° = 1.
- Simplify the equation carefully — combine constants before solving.
- The key trick is multiplying through by 2 at the end to get $x + 2y$ directly. Examiners award 1 mark for correct substitution and 1 mark for the final value.