Exams › SSC CGL (Prelims) › General

If \(\sin A + \cos A = \frac{7}{5}\), find \(\sin 2A\).

1. 9/25
2. 24/25
3. 7/10
4. 12/25

Correct answer: 24/25

Solution

Using \((\sin A+\cos A)^2=\sin^2A+\cos^2A+2\sin A\cos A=1+2\sin A\cos A\). Since \(\sin A+\cos A=\frac{7}{5}\), we get \(\frac{49}{25}=1+2\sin A\cos A\), so \(2\sin A\cos A=\frac{24}{25}\). Hence \(\sin 2A=\frac{24}{25}\).

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