Question

If $3 \tan A = 4$ then the value of $\sec A$ will be

• A. $\dfrac{3}{4}$
• B. $\dfrac{5}{4}$
• C. $\dfrac{3}{5}$
• D. $\dfrac{5}{3}$

Hint:

Always use $\sec^2 A = 1 + \tan^2 A$ for problems linking $\tan A$ and $\sec A$.

Answer 1

The Correct Option is B

Step 1: Given information.
We are given $3 \tan A = 4 \Rightarrow \tan A = \dfrac{4}{3}$.
Step 2: Use trigonometric identity.
We know that: \[ 1 + \tan^2 A = \sec^2 A \] Substitute $\tan A = \dfrac{4}{3}$: \[ 1 + \left(\dfrac{4}{3}\right)^2 = \sec^2 A \] \[ 1 + \dfrac{16}{9} = \sec^2 A \] \[ \sec^2 A = \dfrac{25}{9} \] \[ \sec A = \dfrac{5}{3} \] Step 3: Conclusion.
Hence, $\sec A = \dfrac{5}{3}$.
Correction: The correct option is (D) $\dfrac{5}{3}$.