If 2 sin θ = √3, cos θ = ?

Given:

$2 \sin \theta = \sqrt{3}$

Formula used:

We know the Pythagorean identity: $\sin^2 \theta + \cos^2 \theta = 1$

Calculation:

First, solve for $\sin \theta$ :

$2 \sin \theta = \sqrt{3}$

$\sin \theta = \frac{\sqrt{3}}{2}$

Using the Pythagorean identity:

$\sin^2 \theta + \cos^2 \theta = 1$

$\left( \frac{\sqrt{3}}{2} \right)^2 + \cos^2 \theta = 1$

$\frac{3}{4} + \cos^2 \theta = 1$

$\cos^2 \theta = 1 - \frac{3}{4}$

$\cos^2 \theta = \frac{1}{4}$

$\cos \theta = \pm \frac{1}{2}$

Therefore, the value of $\cos \theta$ is $\pm \frac{1}{2}$ .

So, the correct option is:

2) $\frac{1}{2}$