Question

If \( \frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} = \):

• A. \( \sec A \csc A - 1 \)
• B. \( \tan A + \cot A \)
• C. \( \tan A + \cot A + 1 \)
• D. \( \sec A + \csc A + 1 \)

Hint:

When simplifying trigonometric expressions, use standard identities and common denominators to combine terms.

Answer 1

The Correct Option is C

We are given the equation \( \frac{\tan A}{1 - \cot A} + \frac{\cot A}{1 - \tan A} \). By simplifying the terms using trigonometric identities, we find that the expression simplifies to \( \tan A + \cot A + 1 \).