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SSC CGL 2020 PYQ — Question 72

SSC CGL - 7th March 2020 Shift 3 • Quantitative Aptitude • Q72

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If 5Cos2θ + 1 = 3Sin2θ, 0o < θ < 90o, then what is the value of (tanθ + Secθ)/(Cotθ + Cosecθ)?

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Correct answer: C

Explanation

The correct answer is option 3 i.e (3 + 2√3)/3

⇒ 5Cos2θ + 1 = 3Sin2θ

By adding 3Cos2θ in both the sides

⇒ 5Cos2θ + 1 + 3Cos2θ = 3Sin2θ + 3Cos2θ

⇒ 8Cos2θ + 1 = 3

⇒ Cos2θ = 1 / 4

⇒ Cosθ = 1 / 2 or - 1 / 2

As 0o < θ < 90o Cosθ can not be negative

⇒ θ = 60o

⇒ (tanθ + Secθ) / (Cotθ + Cosecθ)

⇒ (tan60o + Sec60o) / (Cot60o + Cosec60o)

⇒ (√3 + 2) / (1 / √3 + 2 / √3)

⇒ (√3 + 2) / 3 / √3)

⇒ (3 + 2√3) / 3