If \(2\sin 2\theta=\sqrt{3}\), where \(0\le 2\theta\le 90^\circ\), then find the value of \(\cos 3\theta\)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 0
The given equation fixes the value of \(\sin 2\theta\); matching it with a standard angle gives \(2\theta\), and from it \(\theta\) and \(3\theta\).
From \(2\sin 2\theta=\sqrt{3}\): \(\sin 2\theta=\displaystyle\frac{\sqrt{3}}{2}\)
The only angle from \(0^\circ\) to \(90^\circ\) with this sine is \(60^\circ\), so \(2\theta=60^\circ\) and \(\theta=30^\circ\)
Then \(3\theta=90^\circ\), and \(\cos 90^\circ=0\)