Question

If \(\cot A = \dfrac{3}{4}\), then the value of \(\sec A\) will be

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

Hint:

Remember: \(\cot A = \frac{\text{Base}}{\text{Perpendicular}}\) and \(\sec A = \frac{\text{Hypotenuse}}{\text{Base}}\).

Answer 1

The Correct Option is B

Step 1: Given condition.
\[ \cot A = \frac{3}{4} = \frac{\text{Base}}{\text{Perpendicular}} \] Let Base = 3, Perpendicular = 4.
Step 2: Find the hypotenuse.
By Pythagoras theorem: \[ \text{Hypotenuse} = \sqrt{3^2 + 4^2} = \sqrt{9 + 16} = 5 \]
Step 3: Find \(\sec A\).
\[ \sec A = \frac{\text{Hypotenuse}}{\text{Base}} = \frac{5}{4} \]
Step 4: Conclusion.
Hence, the value of \(\sec A\) is \(\dfrac{5}{4}\).