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SSC CHSL 2023 PYQ — Question 56

SSC CHSL - 11 Aug 2023 - Shift 1 • Quantitative Aptitude • Q56

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If cosecθ - cotθ = 72\frac{7}{2}, then the value of Cosecθ will be:

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Correct answer: D

Explanation

The correct answer is option 4 i.e. 5328\frac{53}{28}

cosecθ − cotθ = 7/2
Let’s assume:

cosecθ = x ⇒ cotθ = √(x² − 1) (since cosec²θ − cot²θ = 1)

So,

x − √(x² − 1) = 7/2

⇒ Multiply both sides by 2:

2x − 2√(x² − 1) = 7

⇒ 2x − 7 = 2√(x² − 1)

⇒ Square both sides:

(2x − 7)² = 4(x² − 1)

⇒ 4x² − 28x + 49 = 4x² − 4

−28x + 49 = −4

⇒ −28x = −53

⇒ x = 53/28