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SSC CGL 2019 PYQ — Question 56

SSC CGL Tier II Quant - 12/09/2019 • Quantitative Aptitude • Q56

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If sin⁡2θ−3sin⁡θ+2cos⁡2θ=1{{\sin^2\theta-3\sin\theta+2}\over{\cos^2\theta}} = 1 , where 0 ° < θ < 90°, then what is the value of (cos2θ + sin3θ + cosec2θ) ?

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Correct answer: C

Explanation

The correct answer is option 3 i.e. 9+436{9+4\sqrt3}\over6 .

Let's assume, sinθ = x

⇒ x2−3x+21−x2=1{{x^2-3x+2}\over{1-x^2}} = 1

⇒ (x−1)(x−2)(x−1)(x+1)=−1{{(x-1)(x-2)}\over({x-1})({x+1})} = -1

⇒ (x - 2) = - x - 1

⇒ x + x = -1 + 2

⇒ x = 1/2, sinθ = 1/2, θ = 30°

Now, (cos2θ + sin3θ + cosec2θ) = (1/2) + 1 + (2/√3) = 3+6+436{3+6+4\sqrt3}\over6 = 9+436{9+4\sqrt3}\over6