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SSC CPO 2022 PYQ — Question 119

SSC CPO - 10 Nov 2022 - Shift 1 • Quantitative Aptitude • Q119

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The value of (2cos⁡2θ−2cos⁡θ)(sin⁡θ−2sin⁡2θ)(2 \cos^2\theta - 2\cos\theta)\over(\sin\theta-2\sin^2\theta) is :

Show answer & explanation

Correct answer: C

Explanation

The correct answer is option 3 i.e. cot⁡θ\cot\theta.

The value of (2cos⁡2θ−2cos⁡θ)(sin⁡θ−2sin⁡2θ)(2 \cos^2\theta - 2\cos\theta)\over(\sin\theta-2\sin^2\theta) is :

Formula used 

Cos 2θ = 1 - 2 sin2θ = 2cos2θ - 1

Calculation

= [cos θ (2cos2θ - 1)]/[sinθ (1 - 2 sin2θ)]

= (cosθ × cos2θ)/(sinθ × cos2θ) = cosθ/sinθ = cotθ