Question

If $\tan \alpha + \cot \alpha = 5$, then the value of $\tan^2 \alpha + \cot^2 \alpha$ will be

• A. 27
• B. 28
• C. 23
• D. 25

Hint:

When you see $\tan \alpha + \cot \alpha$, square it to relate to $\tan^2 \alpha + \cot^2 \alpha$ using: \[ (\tan \alpha + \cot \alpha)^2 = \tan^2 \alpha + \cot^2 \alpha + 2 \]

Answer 1

The Correct Option is B

Step 1: Given expression.
We are given: $\tan \alpha + \cot \alpha = 5$.
Step 2: Square both sides.
\[ (\tan \alpha + \cot \alpha)^2 = 25 \] \[ \tan^2 \alpha + \cot^2 \alpha + 2 = 25 \] \[ \tan^2 \alpha + \cot^2 \alpha = 25 - 2 = 23 \] Correct value is 23. Hence, the correct option is (C) 23.