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SSC Selection Post 2020 PYQ — Question 70

SSC Selection Post - Graduation Level 2020 - 9 Nov 2020 - Shift 3 • Quantitative Aptitude • Q70

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If (cosecθ\theta - sinθ\theta) (secθ\theta - cosθ\theta) (tanθ\theta + cotθ\theta) - tanθ\theta= 0, 0°< θ\theta < 90°, then the value of 2cosθ+sinθ5cosθ−sinθ\frac{2cos\theta + sin\theta}{5cos\theta-sin\theta} is:

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 34\frac{3}{4}.

(cosecθ - sinθ)(secθ - cosθ)(tanθ + cotθ) - tanθ = 0 where 0° < θ < 90°

⇒ (cos2θ/sinθ) × (sin2θ/cosθ) × 1/(sinθ cosθ)  - tanθ = 0

⇒ (cosθsinθ)/(sinθcosθ)  - tanθ = 0

⇒ 1 - tanθ = 0

⇒ tanθ = 1

⇒ θ = 45°

Now, (2cos 45° + sin 45°)/(5cos 45° - sin 45°)

= [2(√2/2) + (√2/2)]/[5(√2/2) - (√2/2)]

= (3√2/2)/(4√2/2)

= 3/4