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

Given \( \tan \theta = 2 \), we are to determine \( \sec^2 \theta \).

Step 1: Apply the trigonometric identity The relevant identity is: \[ \sec^2 \theta = 1 + \tan^2 \theta \] 

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

Answer: Thus, \( \sec^2 \theta \) equals \( 5 \). The correct choice is (1).