Exams › SSC CGL (Prelims) › General

If \(\cos 2A = 2\cos^2 A - 1\), then what is the value of \(\sin^2 A\)?

1. \((1 + \cos 2A)/2\)
2. \((1 - \cos 2A)/2\)
3. \(1 - \sin^2 A\)
4. \(\cos^2 A\)

Correct answer: \((1 - \cos 2A)/2\)

Solution

The standard identity is \(\cos 2A = 1 - 2\sin^2 A\). Rearranging gives \(2\sin^2 A = 1 - \cos 2A\), so \(\sin^2 A = \frac{1 - \cos 2A}{2}\).

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