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SSC CPO 2020 PYQ — Question 139

SSC CPO - 23 Nov 2020 - Shift 1 • Quantitative Aptitude • Q139

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If 4 - 2 sin2θ - 5cosθ = 0, 0°< θ < 90°, then the value of cosθ + tanθ is :

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 1+2√32\frac{1+2√3}{2}

4 - 2sin2θ - 5cosθ = 0

4 - 2(1 - cos2θ) - 5cosθ = 0

2cos2θ - 5cosθ + 2 = 0

2cos2θ - 4cosθ - cosθ + 2 = 0

2cosθ (cosθ - 2) - 1(cosθ - 2) = 0

(2cosθ - 1)(cosθ - 2) = 0

cosθ = 1/2

θ = 600

cosθ + tanθ = cos600 + tan600 = 1/2 + √3 = (1 + 2√3)/2