Question

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

• A. \( \tan A + \cot A \)
• B. \( \sec A + \cosec A \)
• C. \( \sin A \cos A + 1 \)
• D. \( \mathbf{\sec A \cosec A + 1} \)

Hint:

Convert all trig identities to sine and cosine, then simplify. Rationalizing helps resolve complex fractions.

Answer 1

The Correct Option is D

Let us simplify both terms: \[ \frac{\cot A}{1 - \tan A} + \frac{\tan A}{1 - \cot A} \] Use \( \cot A = \frac{1}{\tan A} \), substitute and simplify: After rationalizing and simplifying, you get: \[ \sec A \cosec A + 1 \]