Question

If \( \tan \theta = 2 \), then the value of \( \sec^2 \theta \) is:

• A. \( 5 \)
• B. \( 4 \)
• C. \( 3 \)
• D. \( 2 \)

Hint:

When given \( \tan \theta \), use the identity \( \sec^2 \theta = 1 + \tan^2 \theta \) to quickly find \( \sec^2 \theta \).

Answer 1

The Correct Option is A

We are given that \( \tan \theta = 2 \), and we need to find the value of \( \sec^2 \theta \). 

Step 1: Use the trigonometric identity We know the following identity: \[ \sec^2 \theta = 1 + \tan^2 \theta \] 

Step 2: Substitute the given value of \( \tan \theta \) Substitute \( \tan \theta = 2 \) into the identity: \[ \sec^2 \theta = 1 + (2)^2 = 1 + 4 = 5 \] 

Answer: The value of \( \sec^2 \theta \) is \( 5 \), so the correct answer is option (1).