Question

If \[2\sin \theta = \sqrt{3}\]; then:

Options

• \[2\cos \theta + 1 = 0\]

• \[1 - \sin \theta = 0\]

• \[\cos \theta = \sqrt{3}\]

• \[2\cos \theta = 1\]

Answer 1

\[\boldsymbol {2\cos \theta = 1}\]

Explanation:

Given,

\[\Rightarrow 2\sin \theta = \sqrt{3}\]

\[\Rightarrow \sin \theta = \frac{\sqrt{3}}{2}\]

⇒ sin θ = sin 60°

⇒ θ = 60°

⇒ cos θ = cos 60°

⇒ 2 cos θ = 2 cos 60°

\[\Rightarrow 2\cos \theta = 2 \times \frac{1}{2}\]

⇒ 2 cos θ = 1