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SSC CGL 2017 PYQ — Question 92

SSC CGL Tier II Quant - 12/01/2017 • Quantitative Aptitude • Q92

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If x = cosecθ – sinθ and y = secθ – cosθ, then the relation between x and y is:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. x2y2(x2 + y2 + 3) = 1

Application

x = cosecθ – sinθ and y = secθ – cosθ

Put θ = 45°

⇒ x = cosec 45° – sin 45°

⇒ x = √2 – 1/√2

⇒ x = 1/√2

And

y = sec 45° – cos 45°

⇒ y = √2 – 1/√2

⇒ y = 1/√2

Now, check with the options:

Option 2:

x2y2(x2 + y2 + 3) = 1

Put x = 1/√2 and y = 1/√2:

So,

⇒ 1/2 × 1/2 × (1/2 + 1/2 + 3) = 1

⇒ 1 = 1

It is satisfied hence option 2 is correct.