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SSC Selection Post 2022 PYQ — Question 69

SSC Selection Post - Graduation Level - 8 Feb 2022 - Shift 3 • Quantitative Aptitude • Q69

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If secθ+tanθsecθ−tanθ=53 {sec \theta + tan \theta \over sec \theta - tan \theta} = {5 \over 3} 0°< θ < 90°, then what is the value of (cosec θ + cos θ + cot θ)?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 16+5154{16 +5 \sqrt{15} \over 4}.

(secθ + tanθ)/(secθ - tanθ) = 5/3

⇒ 3secθ + 3tanθ = 5secθ - 5tanθ

⇒ 8tanθ = 2secθ

⇒ 4(sinθ/cosθ) = 1/cosθ

⇒ sinθ = 1/4

⇒ cosθ = √(1 - sin²θ) = √(15/16) = √15/4

⇒ tanθ = sinθ/cosθ = (1/4)/(√15/4) = 1/√15

So, cosecθ + cosθ + cotθ = 4 + √15/4 + √15 = 16+5154{16 +5 \sqrt{15} \over 4}