If sin A + cos A =5over4 , find sin 2A.

If $sin A + cos A ={5\over4}$ , find sin 2A.

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Correct answer: D

Explanation

The correct answer is option 4 i.e. $9\over16$ .

sin A + cos A = 5/4

⇒ (sin A + cos A)² = sin²A + cos²A + 2 sinA cosA = 1 + sin 2A

⇒ 1 + sin 2A = (5/4)² = 25/16

⇒ sin 2A = 25/16 – 1 = 9/16

SSC CGL 2025 PYQ — Question 54