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mediumMCQStaff Selection Commission2026Quantitative Aptitude
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If
(secA−1)
2

tan
2
A
​
=x, then the value of x is:

  1. A
    \frac{1+\csc A}{1-\csc A}
  2. B
    (1+\cos A)(1-\cos A)
  3. C
    \frac{1+\cos A}{1-\cos A}
  4. D
    (1+\csc A)(1-\csc A)

Solution & Step-by-step Explanation

Given expression:
x=
(secA−1)
2

tan
2
A
​

We know that tan
2
A=sec
2
A−1=(secA−1)(secA+1).
Substitute this into the expression:

x=
(secA−1)
2

(secA−1)(secA+1)
​

x=
secA−1
secA+1
​

Convert secA to
cosA
1
​
:

x=
cosA
1
​
−1
cosA
1
​
+1
​
=
cosA
1−cosA
​

cosA
1+cosA
​

​
=
1−cosA
1+cosA
​

Practice this question

Try it yourself before checking the explanation above.

If
(secA−1)
2

tan
2
A
​
=x, then the value of x is:
A
\frac{1+\csc A}{1-\csc A}
B
(1+\cos A)(1-\cos A)
C
\frac{1+\cos A}{1-\cos A}
D
(1+\csc A)(1-\csc A)

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