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SSC CGL 2025 PYQ — Question 58

SSC CGL - 22 Sep 2025 - Shift 3 • Quantitative Aptitude • Q58

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If sin A + cos A = 22\frac{\sqrt{2}}{2}, find the value of sin2A + cos2A + 2sinAcosA.

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 12\frac{1}{2}.

sin⁡A+cos⁡A=22\sin A + \cos A = \frac{\sqrt{2}}{2}

⇒ (sin⁡A+cos⁡A)2=24=12(\sin A + \cos A)^2= {2 \over 4} ={1 \over 2}

⇒ sin⁡2A+cos⁡2A+2sin⁡Acos⁡A=12\sin^2 A + \cos^2 A + 2\sin A \cos A={1 \over 2}