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SSC CGL 2024 PYQ — Question 51

SSC CGL - 23 Sep 2024 - Shift 2 • Quantitative Aptitude • Q51

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If sinA - cosA = 3−22{ \sqrt{3} - \sqrt{2} \over 2} , then the value of sinA.cosA is :

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Correct answer: C

Explanation

The correct answer is option 3 i.e.  26−18{ 2\sqrt{6} - 1 \over 8}.

sin2A + cos2A = 1

Given,  sinA - cosA = 3−22{ \sqrt{3} - \sqrt{2} \over 2} 

Squarying both sides,

(sinA - cosA)2 = (3−22)2({ \sqrt{3} - \sqrt{2} \over 2})^2

⇒ sin2A + cos2A - 2sinAcosA = 5−264{5 - 2\sqrt{6}}\over 4

⇒ 1 - 2sinAcosA = 5−264{5 - 2\sqrt{6}}\over 4

⇒ 2sinAcosA = 1 - 5−264{5 - 2\sqrt{6}}\over 4

⇒ 2sinAcosA = 26−14{2 \sqrt{6} - 1}\over 4

⇒ sinAcosA = 26−18{2 \sqrt{6} - 1}\over 8