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SSC CHSL 2021 PYQ — Question 56

SSC CHSL - 19 April 2021 - Shift 2 • Quantitative Aptitude • Q56

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If sinθ=2aba+b\theta=\frac{2\sqrt{ab}}{a+b}, a > b > 0, then the value of cosθ+1cosθ−1​\frac{cos\theta + 1}{ cos\theta-1 } ​ will be:

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Correct answer: B

Explanation

The correct answer is option 2 i.e. −ab-\frac{a}{b}

Concept USed:

sinA = PHP \over H

cosA = BHB \over H

H2 = P2 + B2 

Explanation:

According to the given question,

sin⁡θ=2aba+b\sin \theta=\frac{2\sqrt{ab}}{a+b}

⇒ P = 2ab2\sqrt{ab} and H = a + b

Now, H2 = P2 + B2 

⇒ B2 = H2 - P2 

⇒ B2 = (a + b)2 - 4ab

⇒ B2 = a2 + b2 + 2ab - 4ab

⇒ B2 = a2 + b2 - 2ab

⇒ B2 = (a - b)2

⇒ B = a - b

Now, cos⁡θ=(a−b)(a+b)\cos\theta = {(a - b) \over (a + b)}

Now, required value = (a−b)(a+b)+1(a−b)(a+b)−1​\frac{{(a - b) \over (a + b)} +1}{{(a -b)\over (a + b)}-1 } ​ = 2a−2b​\frac{2a}{-2b} ​ = −ab-\frac{a}{b}

HEnce the required answer is −ab-\frac{a}{b}