Exams › SSC CGL (Prelims) › General

If csc A - cot A = q, then csc A expressed in terms of q is:

1. (q^2 + 1) / (2q)
2. (q^2 - 1) / (2q)
3. (q^2 + 1) / q
4. (q^2 - 1) / q

Correct answer: (q^2 + 1) / (2q)

Solution

Since csc^2 A - cot^2 A = 1 = (cscA - cotA)(cscA + cotA), and cscA - cotA = q, we get cscA + cotA = 1/q. Adding gives 2 cscA = q + 1/q, so cscA = (q^2 + 1)/(2q).

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