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SSC CGL 2025 PYQ — Question 58

SSC CGL - 22 Sep 2025 - Shift 2 • Quantitative Aptitude • Q58

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If sin A = 23\frac{2}{3}, find the value of (3sin A - 4cos A)2 + (4sinA + 3cos A)2.

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 25.

Let p = sin A, q = cos A

sin A = 2/3 ⇒ sin2A = 4/9

cos A = √(1 – sin2A) = √(1 – 4/9) = √(5/9) = √5/3

So sin2A + cos2A = p2 + q2 = 1

(3sin A - 4cos A)2 + (4sinA + 3cos A)2

= (3p – 4q)2 + (4p + 3q)2

= 9p2 + 16q2 – 24pq + 16p2 + 9q2 + 24pq

= 25p2 + 25q2

= 25(p2 + q2)

= 25 × 1

= 25