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SSC CGL 2025 PYQ — Question 52

SSC CGL - 20 Sep 2025 - Shift 3 • Quantitative Aptitude • Q52

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If sin⁡A=513\sin A = {5\over13}, find the value of sin4A + cos4A.

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 2136128561\frac{21361}{28561}.

sin2A = (5/13)2 = 25/169

⇒ cos A = √(1 - sin2A) = √(1 – 25/169) = √(144/169) = 12/13

⇒ cos2A = (12/13)2 = 144/169

sin4A + cos4A = (sin2A)2 + (cos2A)2

= (25/169)2 + (144/169)2

= (252 + 1442)/1692

= (625 + 20736)/28561

= 21361/28561