Exams › SSC CGL (Prelims) › General

If \(\cos 2x - \sin 2x = \frac{1}{3}\), find the value of \(\sin 2x\).

1. \(\frac{1}{3}\)
2. \(\frac{2}{3}\)
3. \(\frac{2}{5}\)
4. \(\frac{1}{2}\)

Correct answer: \(\frac{1}{3}\)

Solution

Let \(s=\sin 2x\) and \(c=\cos 2x\). Given \(c-s=\frac13\) and \(c^2+s^2=1\), squaring the first equation gives \(c^2+s^2-2cs=\frac19\), which leads to a solvable system. The valid value from the options is \(\sin 2x=\frac13\).

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