Question

If \(2\tan A = 3\), then value of \(\sec A\) equals

• A. \(\frac{\sqrt{13}}{2}\)
• B. \(\frac{\sqrt{13}}{4}\)
• C. \(\frac{2}{\sqrt{13}}\)
• D. \(\frac{\sqrt{13}}{2}\)

Hint:

Alternatively, use a right triangle. If \(\tan A = 3/2\), the opposite side is 3 and adjacent side is 2. The hypotenuse is \(\sqrt{3^2 + 2^2} = \sqrt{13}\). Thus, \(\sec A = \text{hypotenuse} / \text{adjacent} = \sqrt{13}/2\).

Answer 1

The Correct Option is A

To solve the problem of finding the value of \(\sec A\) when given \(2\tan A = 3\), we will follow the steps below:

1. First, express \(\tan A\) from the given equation:

\(\tan A = \frac{3}{2}\)

1. We know the trigonometric identity involving \(\tan A\) and \(\sec A\):

\(\sec^2 A = 1 + \tan^2 A\)

1. Substitute \(\tan A = \frac{3}{2}\) into the identity:

\(\sec^2 A = 1 + \left(\frac{3}{2}\right)^2 = 1 + \frac{9}{4} = \frac{13}{4}\)

1. Taking the square root of both sides gives:

\(\sec A = \sqrt{\frac{13}{4}} = \frac{\sqrt{13}}{2}\)

1. Therefore, the value of \(\sec A\) is:

\(\frac{\sqrt{13}}{2}\)

1. Hence, the correct option is:

\(\frac{\sqrt{13}}{2}\)