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SSC CHSL 2023 PYQ — Question 68

SSC CHSL - 09 Aug 2023 - Shift 2 • Quantitative Aptitude • Q68

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The given expression is equal to:sin4A+cos4A1−2sin2Acos2A\frac{sin^4 A+ cos^4 A}{1-2sin^2 A cos² A } 

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Correct answer: A

Explanation

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

sin4A+cos4A1−2sin2Acos2A\frac{sin^4 A+ cos^4 A}{1-2sin^2 A cos² A }

=(sin2A+cos2A)2−2sin2Acos2A1−2sin2Acos2A=\frac{(sin^2A + cos^2A)^2 - 2 sin^2A cos^2A}{1-2sin^2 A cos² A }

=12−2sin2Acos2A1−2sin2Acos2A=\frac{1^2 - 2 sin^2A cos^2A}{1-2sin^2 A cos² A }

=1−2sin2Acos2A1−2sin2Acos2A=\frac{1 - 2 sin^2A cos^2A}{1-2sin^2 A cos² A }

= 1

Therefore, the value of the given expression is 1.