Question:
In a right-angled triangle, if \(\sin \theta = \dfrac{1}{2}\), find the value of \(2 \sin \theta \cos \theta\).
एक समकोण त्रिभुज में, यदि \(\sin \theta = \dfrac{1}{2}\) है, तो \(2 \sin \theta \cos \theta\) का मान ज्ञात कीजिए।
Options:
- \(\dfrac{\sqrt{3}}{2}\)
- \(\dfrac{1}{2}\)
- \(\dfrac{\sqrt{3}}{4}\)
- \(\dfrac{3}{4}\)
- \(\dfrac{\sqrt{3}}{2}\)
- \(\dfrac{1}{2}\)
- \(\dfrac{\sqrt{3}}{4}\)
- \(\dfrac{3}{4}\)
Correct Answer: a)
Explanation:
Since \(\sin \theta = \dfrac{1}{2}\), \(\theta = 30^\circ\).
Then \(\cos 30^\circ = \dfrac{\sqrt{3}}{2}\).
\(2 \sin \theta \cos \theta = \sin 2\theta = \sin 60^\circ = \dfrac{\sqrt{3}}{2}\).
\(\sin \theta = \dfrac{1}{2} \implies \theta = 30^\circ\).
\(2 \sin \theta \cos \theta = \sin 2\theta = \sin 60^\circ = \dfrac{\sqrt{3}}{2}\)।