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SSC CGL 2017 PYQ — Question 86

SSC CGL Tier II Quant - 12/01/2017 • Quantitative Aptitude • Q86

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If secA + tanA = a, then the value of cosA is:

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Correct answer: B

Explanation

  The correct answer is option 2 i.e. 2a/(a2 + 1)

Understanding

Application

We know:

Sec2x – Tan2x = 1

Sec2A – Tan2A = 1

(sec A + tan A)(sec A – tan A) = 1

Given:

sec A + tan A = a

So,

(sec A – tan A) = 1/a

Adding both the equations:

2sec A = a + 1/a

sec A = (a2 + 1)/2a

Or

cos A = 2a/(a2 + 1)