Question

If \(\tan \theta + \cot \theta = 2\), then \(\tan^2 \theta + \cot^2 \theta =\)

• A. 4
• B. 2
• C. 6
• D. 1

Answer 1

The Correct Option is B

Correct answer: 2 

Explanation:
Given: \[ \tan \theta + \cot \theta = 2 \] We need to find \( \tan^2 \theta + \cot^2 \theta \). Using the identity: \[ (\tan \theta + \cot \theta)^2 = \tan^2 \theta + \cot^2 \theta + 2 \] Substituting \( \tan \theta + \cot \theta = 2 \): \[ 2^2 = \tan^2 \theta + \cot^2 \theta + 2 \] \[ 4 = \tan^2 \theta + \cot^2 \theta + 2 \] \[ \tan^2 \theta + \cot^2 \theta = 4 - 2 = 2 \]

Hence, \( \tan^2 \theta + \cot^2 \theta = {2} \).