If ^2 A/(A - 1)^2 = x , then the value of x is: - Quantitative Aptitude MCQ Competitive Exams 2026 | ExamTest.live

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If \frac{t a n ^{2} A}{( s e c A - 1 ) ^{2}} = x, then the value of x is:

Solution & Step-by-step Explanation

Given expression: x = \frac{tan ^{2} A}{( sec A - 1 ) ^{2}} Using the identity tan^{2} A = sec^{2} A - 1 = (sec A - 1) (sec A + 1) : x = \frac{( sec A - 1 ) ( sec A + 1 )}{( sec A - 1 ) ^{2}} x = \frac{sec A + 1}{sec A - 1} Convert sec A into terms of cos A where sec A = \frac{1}{c o s A} : x = \frac{\frac{1}{c o s A} + 1}{\frac{1}{c o s A} - 1} x = \frac{\frac{1 + c o s A}{c o s A}}{\frac{1 - c o s A}{c o s A}} x = \frac{1 + cos A}{1 - cos A}

Try it yourself before checking the explanation above.

If \frac{t a n ^{2} A}{( s e c A - 1 ) ^{2}} = x, then the value of x is:

\frac{1+\csc A}{1-\csc A}

(1+\cos A)(1-\cos A)

\frac{1+\cos A}{1-\cos A}

(1+\csc A)(1-\csc A)

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