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SSC CHSL 2021 PYQ — Question 58

SSC CHSL - 19 April 2021 - Shift 1 • Quantitative Aptitude • Q58

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If sinθ(2sinθ+3)=2,0°<θ<90°,{{sin\theta(2 sin\theta+3)=2,0°<\theta<90°,}}then what is the value of (sec2θ+cot2θ−cos2θ)?({{sec^2\theta+cot^2\theta-cos^2\theta)?}}

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Correct answer: A

Explanation

The correct answer is Option 1 i.e. 4312{{43} \over 12}

sinθ(2sinθ+3)=2,0°<θ<90°,{{sin\theta(2 sin\theta+3)=2,0°<\theta<90°,}}

2sin2θ + 3sinθ - 2 = 0

Let's assume  θ = 30°

2 × (1/4) + 3/2 - 2 = 0

1/2 + 3/2 - 2 = 0

0 = 0

So, the value of (sec2θ+cot2θ−cos2θ)({{sec^2\theta+cot^2\theta-cos^2\theta)}}

4/3 + 3 - 3/4

= (16 + 36 - 9)/12 

= 43/12