Mathematics — Standard (041) — CBSE Class 10 board question

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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• 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.