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SSC CGL 2024 PYQ — Question 58

SSC CGL - 11 Sep 2024 - Shift 3 • Quantitative Aptitude • Q58

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If psin A − cos A = 1, then p2 − (1 + p2) cos A equals:

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Correct answer: A

Explanation

The correct answer is option 1 i.e. 1.

psin A − cos A = 1

⇒ psin A = 1 + cos A

⇒ p = (1 + cos A)/sin A

Now, according to the question;

⇒ p2 − (1 + p2) × cos A

⇒ [(1 + cos A)2/sin2A] - (1 + (1 + cos A)2/sin2A) × cos A         ---- (1)

We know that

sin2 = (1 - cos2A) = (1 + cos A)(1 - cos A)            ---- (2)

Using equation (2) in (1), we get

⇒ [(1 + cos A)2/(1 + cos A)(1 - cos A)] - (1 + (1 + cos A)2/(1 + cos A)(1 - cos A)) × cos A

⇒ [(1 + cos A)/(1 - cos A)] - (1 + (1 + cos A)/(1 - cos A)) × cos A

⇒ [(1 + cos A)/(1 - cos A)] - (2cos A/(1 - cos A))

⇒ (1 + cos A - 2cos A)/(1 - cos A)

⇒ (1 - cos A)/(1 - cos A) = 1