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SSC Selection Post 2022 PYQ — Question 59

SSC Selection Post - Graduation Level - 9 Feb 2022 - Shift 3 • Quantitative Aptitude • Q59

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If 14 sin2θ + 3 sinθ - 5 = 0, 0° < θ < 90°, then the value of sec2θ+cot2θcosec2θ+tan2θsec2θ+cot2θ\over{cosec2θ+tan2θ} is:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 1+2351+2\sqrt3\over5.

14sin2θ + 3sinθ - 5 = 0

⇒ sinθ = [-3 ± √(9 + 280)]/28 = [-3 ± 17]/28

⇒ sinθ = (-3 + 17)/28 = 14/28 = 0.5

⇒ θ = 30°

Now, sec2θ+cot2θcosec2θ+tan2θ=sec60∘+cot60∘cosec60∘+tan60∘{sec2θ+cot2θ\over{cosec2θ+tan2θ}}={sec60^\circ+cot60^\circ\over{cosec60^\circ+tan60^\circ}}

= [2 + (1/√3)]/[(2/√3) + √3]

= [(2√3 + 1)/√3]/[(2 + 3)/√3]

= (1 + 2√3)/5