Question:
\(\frac{\cot A}{1 - \tan A} + \frac{\tan A}{1 - \cot A} =\)
\(\frac{\cot A}{1 - \tan A} + \frac{\tan A}{1 - \cot A} =\)
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Convert all trig identities to sine and cosine, then simplify. Rationalizing helps resolve complex fractions.
Updated On: May 15, 2025
- \( \tan A + \cot A \)
- \( \sec A + \cosec A \)
- \( \sin A \cos A + 1 \)
- \( \mathbf{\sec A \cosec A + 1} \)
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The Correct Option is D
Solution and Explanation
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:
\[
\sec A \cosec A + 1
\]
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