Q1. [1] § 8.3 Trigonometric Ratios of Some Specific Angles § 8.5 Summary
If $\sin\theta = 1$, then the value of $\dfrac{1}{2}\sin\left(\dfrac{\theta}{2}\right)$ is :
- A $\dfrac{1}{2\sqrt{2}}$
- B $\dfrac{1}{2}$
- C $\dfrac{1}{2}$
- D 0
Previously asked in CBSE board exam
2024 30/4/1 Q10
Generated by claude-sonnet-4-6 · 2026-06-15 10:23 · grounding rag
Model Answer
Option (A) $\dfrac{1}{2\sqrt{2}}$
Since $\sin\theta = 1$, we get $\theta = 90°$, so $\dfrac{\theta}{2} = 45°$.
Therefore, $\dfrac{1}{2}\sin 45° = \dfrac{1}{2} \times \dfrac{1}{\sqrt{2}} = \dfrac{1}{2\sqrt{2}}$.
Source: Chapter 8, Section 8.3
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Explanation
- The key step is recognising $\sin\theta = 1 \Rightarrow \theta = 90°$, hence $\theta/2 = 45°$.
- From Table 8.1, $\sin 45° = \dfrac{1}{\sqrt{2}}$; multiplying by $\dfrac{1}{2}$ gives $\dfrac{1}{2\sqrt{2}}$.
- Note: Options B and C appear identical ($\dfrac{1}{2}$) — a likely misprint in the paper; the correct answer is unambiguously A.
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