The expression A/1 - A + A/1 - A can be written as: - Mathematics MCQ JEE Main 2026 | ExamTest.live

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1 mark

The expression \frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A} can be written as:

Solution & Step-by-step Explanation

Convert to sine and cosine: \frac{sin A / cos A}{1 - cos A / sin A} + \frac{cos A / sin A}{1 - sin A / cos A} = \frac{sin ^{2} A}{cos A ( sin A - cos A )} - \frac{cos ^{2} A}{sin A ( sin A - cos A )} = \frac{sin ^{3} A - cos ^{3} A}{sin A cos A ( sin A - cos A )} = \frac{( sin A - cos A ) ( sin ^{2} A + sin A cos A + cos ^{2} A )}{sin A cos A ( sin A - cos A )} = \frac{1 + sin A cos A}{sin A cos A} = \frac{1}{sin A cos A} + 1 = sec A csc A + 1 .

Try it yourself before checking the explanation above.

The expression \frac{t a n A}{1 - c o t A} + \frac{c o t A}{1 - t a n A} can be written as:

\sec A \csc A + 1

\tan A + \cot A

\sec A + \csc A

\sin A \cos A + 1

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