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SSC CGL 2019 PYQ — Question 55

SSC CGL - 7th June 2019 - Shift 3 • Quantitative Aptitude • Q55

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If 1/(Cosecθ - 1) + 1/(Cosecθ + 1) = 2Secθ, 00 < θ < 900, then the value of (Cotθ + Cosθ) is:

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Correct answer: B

Explanation

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

⇒ 1/(Cosecθ - 1) + 1/(Cosecθ + 1) = 2Secθ

⇒ (Cosecθ + 1 + Cosecθ - 1)/((Cosecθ - 1)(Cosecθ + 1)) = 2Secθ

⇒ 2Cosecθ/Cot2θ = 2Secθ

⇒ Cotθ = Cot2θ

⇒ Cotθ = 0 or Cotθ = 1

⇒ θ = 90o or θ = 45o

⇒ θ ≠ 90o, θ = 45o

⇒ Cotθ + Cosθ

⇒ 1 + (1/√2)

⇒ (2 + √2)/2