Question

If tan A = √3, then the value of Sec A will be :

• A. 4
• B. 3
• C. 2
• D. 1/2

Hint:

Always check if the given value corresponds to a standard angle like $30^\circ, 45^\circ,$ or $60^\circ$ first!

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
We can solve this using the trigonometric identity $1 + \tan^2 A = \sec^2 A$ or by identifying the angle $A$ from standard trigonometric tables.

Step 2: Method 1 (Identifying the Angle):
We know that $\tan 60^\circ = \sqrt{3}$. Therefore, $A = 60^\circ$.
Now, we find $\sec 60^\circ$:
$$\sec 60^\circ = \frac{1}{\cos 60^\circ} = \frac{1}{1/2} = 2$$
Step 3: Method 2 (Identity):
$$\sec^2 A = 1 + \tan^2 A = 1 + (\sqrt{3})^2$$
$$\sec^2 A = 1 + 3 = 4$$
$$\sec A = \sqrt{4} = 2$$
Step 4: Final Answer:
The value of $\sec A$ is 2.