Question

If tanθ+cotθ = 5, then tan²θ+ cot²θ =?

• A. 27
• B. 25
• C. 24
• D. 23

Answer 1

The Correct Option is D

Given: \[ \tan \theta + \cot \theta = 5 \] We want to find \( \tan^2 \theta + \cot^2 \theta \). Using the identity: \[ (\tan \theta + \cot \theta)^2 = \tan^2 \theta + \cot^2 \theta + 2 \] Substitute the given value: \[ 5^2 = \tan^2 \theta + \cot^2 \theta + 2 \] \[ 25 = \tan^2 \theta + \cot^2 \theta + 2 \] \[ \tan^2 \theta + \cot^2 \theta = 25 - 2 = 23 \]

The correct option is (D): \(23\)