Exams › SSC CGL (Prelims) › General

If sin(A) = (m^2 - n^2) / (m^2 + n^2), what is cos(A)?

1. 2mn / (m^2 + n^2)
2. 2mn / (m^2 - n^2)
3. (m^2 + n^2) / (2mn)
4. (m^2 - n^2) / (2mn)

Correct answer: 2mn / (m^2 + n^2)

Solution

cos(A) = sqrt(1 - sin^2 A). Here 1 - (m^2-n^2)^2/(m^2+n^2)^2 = [(m^2+n^2)^2 - (m^2-n^2)^2]/(m^2+n^2)^2 = 4m^2 n^2/(m^2+n^2)^2, whose square root is 2mn/(m^2+n^2).

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