Question

If \(\sec \theta = \frac{2}{\sqrt{3}}\),then \(cosθ=\)

• A. \(\frac{\sqrt{3}}{2}\)
• B. \(\frac{2}{\sqrt{3}}\)
• C. \(\frac{1}{\sqrt{2}}\)
• D. \(\frac{1}{\sqrt{3}}\)

Answer 1

The Correct Option is A

To solve the problem, we are given the value of $\sec \theta$ and are asked to find the value of $\cos \theta$.

1. Understanding the Identity:
By definition, the secant function is the reciprocal of the cosine function:

$ \sec \theta = \frac{1}{\cos \theta} $

2. Substituting the Given Value:
We are given:
$ \sec \theta = \frac{2}{\sqrt{3}} $
So,
$ \cos \theta = \frac{1}{\sec \theta} = \frac{1}{\frac{2}{\sqrt{3}}} = \frac{\sqrt{3}}{2} $

Final Answer:
$ \cos \theta = \frac{\sqrt{3}}{2}