Question

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

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

Hint:

Using the identity \(\sec A = \sqrt{1 + \tan^2 A}\) is much faster than drawing a right-angled triangle and avoids potential arithmetic errors.
Always keep basic Pythagorean identities memorized for speed!

Answer 1

The Correct Option is D

Step 1: Build a right triangle from the given ratio.
Since $\tan A = \frac{3}{2}$, take the side opposite to $A$ as $3$ and the side adjacent to $A$ as $2$.
Step 2: Find the hypotenuse using Pythagoras.
\[ \text{Hypotenuse} = \sqrt{3^2 + 2^2} = \sqrt{13} \]
Step 3: Read off sec A directly from the triangle.
\[ \sec A = \frac{\text{Hypotenuse}}{\text{Adjacent}} = \frac{\sqrt{13}}{2} \]
\[ \boxed{\sec A = \frac{\sqrt{13}}{2}} \]