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SSC CGL 2022 PYQ — Question 90

SSC CGL Tier II - Quant - 29 Jan 2022 • Quantitative Aptitude • Q90

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If 1 + 2tan2 θ + 2sinθ sec2 θ = ab\frac{a}{b}, 0º < θ < 90º, then a+ba−b\frac{a+b}{a-b}=?

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Correct answer: B

Explanation

 The correct answer is option 2 i.e. cosecθ

⇒ 1 + 2tan2 θ + 2sinθsec2 θ = a/b

⇒ 1 + 2 × sin2θ/cos2θ + 2 × sinθ/cos2θ = a/b

⇒ (cos2θ + 2sin2θ + 2sinθ)/cos2θ = a/b

⇒ (1 - sin2θ + 2sin2θ + 2sinθ)/cos2θ = a/b

⇒ (1 - sinθ)2/(1 - sin2θ) = a/b

⇒ (1 + sinθ)/(1 - sinθ) = a/b

⇒ a = 1 + sinθ and b = 1 - sinθ

⇒ (a + b)/(a - b) = 2/2sinθ = cosecθ.