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SSC Selection Post 2022 PYQ — Question 57

SSC Selection Post - Higher Secondary Level - 08 Feb 2022 - Shift 2 • Quantitative Aptitude • Q57

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If cos2θ – sin2θ – 3cosθ + 2 = 0, 0° < θ < 90° ,then what is the value of 5cosθ - tanθ2 {tan\theta{} \over 2}

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 5−32{5 - \sqrt{3} \over 2}.

cos2θ - sin2θ - 3cosθ + 2 = 0

⇒ cos(2θ) - 3cosθ + 2 = 0

⇒ (2cos2θ - 1) - 3cosθ + 2 = 0

⇒ 2cos2θ - 3cosθ + 1 = 0

⇒ (2cosθ - 1)(cosθ - 1) = 0

⇒ cosθ = 1/2

⇒ θ = 60°

5cosθ - (tanθ)/2 = 5(1/2) - (√3/2) = (5 - √3)/2