Question

If \( \sin \theta = \sqrt{2} \cos \theta \), then the value of \( \sec \theta \) is:

• A. \( \frac{1}{\sqrt{3}} \)
• B. \( \sqrt{3} \)
• C. \( \frac{\sqrt{3}}{2} \)
• D. \( \frac{2}{\sqrt{3}} \)

Hint:

Using the Pythagorean identity: \[ 1 + \tan^2 \theta = \sec^2 \theta. \] For \( \tan \theta = k \), we find: \[ \sec \theta = \sqrt{1 + k^2}. \]

Answer 1

The Correct Option is B

Given equation:
\[ \sin \theta = \sqrt{2} \cos \theta. \] Dividing both sides by \( \cos \theta \):
\[ \tan \theta = \sqrt{2}. \] Using the identity \( \sec^2 \theta = 1 + \tan^2 \theta \):
\[ \sec^2 \theta = 1 + 2 = 3. \] \[ \sec \theta = \sqrt{3}. \] Thus, the correct answer is:
\[ \sqrt{3}. \]