Exams › SSC CGL (Prelims) › General

If \(\sin A = \frac{m^2-n^2}{m^2+n^2}\), what is \(\cos A\)?

1. \(\frac{2mn}{m^2+n^2}\)
2. \(\frac{2mn}{m^2-n^2}\)
3. \(\frac{m^2+n^2}{2mn}\)
4. \(\frac{m^2-n^2}{2mn}\)

Correct answer: \(\frac{2mn}{m^2+n^2}\)

Solution

The given sine value matches the standard identity \(\sin A = \frac{m^2-n^2}{m^2+n^2}\), for which the corresponding cosine is \(\frac{2mn}{m^2+n^2}\). This is a standard Pythagorean-triple-based trigonometric form.

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