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SSC CHSL 2021 PYQ — Question 75

SSC CHSL - 16 April 2021 - Shift 2 • Quantitative Aptitude • Q75

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If sin θ=1213,\theta = \frac{12}{13}, then sin2θ−cos2θ2cosθsinθ×cot2θ=?\frac{sin^2\theta-cos^2\theta}{2cos\theta sin \theta}\times cot^2\theta=?

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 5953456\frac{595}{3456}

Given that

if sinθ=1213,\theta = \frac{12}{13},

By Pythagoras Triplet

cos θ = 5/13 , cot θ = 5/12 , sin 2θ = 2 sinθ cosθ = 2 * (12/13) * (5/13) = 120/169

Now these values are put into the equation

sin2θ−cos2θ2cosθsinθ×cot2θ=?\frac{sin^2\theta-cos^2\theta}{2cos\theta sin \theta}\times cot^2\theta=?

= {(12/13)2 - (5/13)2 } * (5/12)2/(120/169)

= {(144 - 25) * 25 * 169}/(169* 144* 120)

= (119 * 5)/ (144 *24)

= 5953456\frac{595}{3456}