Question

If \(2\sin2\theta=\sqrt3\), where 0 ≤ 2θ ≤ 90°, then find the value of cos 3θ

• A. 0
• B. 1
• C. \(\frac{\sqrt3}{2}\)
• D. \(\frac{1}{2}\)

Answer 1

The Correct Option is A

To solve the problem, we need to find the value of \( \cos 3\theta \) given \( 2\sin 2\theta = \sqrt{3} \) and \(0 \leq 2\theta \leq 90^\circ\).
First, solve for \(\sin 2\theta\):

\( \sin 2\theta = \frac{\sqrt{3}}{2} \)

In the interval \(0 \leq 2\theta \leq 90^\circ\), \(\sin 2\theta = \frac{\sqrt{3}}{2}\) corresponds to \(2\theta = 60^\circ\). Therefore, \(\theta = 30^\circ\).

Now, calculate \(\cos 3\theta\):

\[\cos 3\theta = \cos (90^\circ)\]

Using the identity, \(\cos 90^\circ = 0\), we find:

Thus, \(\cos 3\theta = 0\).

The correct answer is 0.