Exams › SSC CGL (Prelims) › General

If cos A = m/n, what is the value of (1 + cot^2 A)?

1. n^2 / (n^2 - m^2)
2. 2n^2 / (n^2 - m^2)
3. n^2 / [2(n^2 - m^2)]
4. 5n^2 / (n^2 - m^2)

Correct answer: n^2 / (n^2 - m^2)

Solution

Using 1 + cot^2 A = cosec^2 A = 1/sin^2 A, and sin^2 A = 1 - m^2/n^2 = (n^2 - m^2)/n^2, the value is n^2/(n^2 - m^2).

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