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SSC Selection Post 2022 PYQ — Question 73

SSC Selection Post - Graduation Level 2022 - 10 Feb 2022 - Shift 3 • Quantitative Aptitude • Q73

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If 8cos2θ - 2cosθ - 3 = 0, 0° < θ < 90°, then what is the value of 3 tanθ + cosecθ +  cotθ?

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 27\sqrt7.

8cos2θ - 2cosθ - 3 = 0, where 0° < θ < 90°

⇒ cosθ = [2 ± √(4 + 96)]/16

⇒ cosθ = 3/4

sinθ = √(1 - cos2θ) = √(1 - 9/16) = √7/4

tanθ = sinθ/cosθ = (√7/4)/(3/4) = √7/3

cosecθ = 1/sinθ = 4/√7 = (4√7)/7

Now, 3tanθ + cosecθ + cotθ = 3(√7/3) + (4√7)/7 + (3√7)/7 = 2√7