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SSC CGL 2023 PYQ — Question 67

SSC CGL - 20 July 2023 - Shift 1 • Quantitative Aptitude • Q67

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Solve the given expression.sec2(900−θ)−cot2θ2(sin2350+sin2550)\frac{sec^2(90^0-\theta)-cot^2\theta}{2(sin^235^0+sin^255^0)}

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 0.5.

⇒ sec2(900−θ)−cot2θ2(sin2350+sin2550)\frac{sec^2(90^0-\theta)-cot^2\theta}{2(sin^235^0+sin^255^0)} 

⇒ cosec2θ−cot2θ2(sin2(900−350)+sin2550)\frac{cosec^2\theta-cot^2\theta}{2(sin^2(90^0 -35^0)+sin^255^0)}

⇒ cosec2θ−cot2θ2(cos2550+sin2550)\frac{cosec^2\theta-cot^2\theta}{2(cos^255^0+sin^255^0)}  [cos2x + sin2x = 1]

⇒ 12×1\frac{1}{2\times1} = 12=0.5{1\over2} = 0.5