If Cosec θ – Cot θ = 1/4 then the value of Cosec θ + Cot θ isA

1.	If Cosec θ – Cot θ = 1/4 then the value of Cosec θ + Cot θ isA) 1 B) -1 C) 1/4 D) 4
Answer» Correct option is: D) 4 Given that Cosec \(\theta\) – Cot \(\theta\) = \(\frac 14\) ...(1) \(\therefore\) ( cosec \(\theta\) - cot \(\theta\)) (cosec \(\theta\) + cot \(\theta\)) = \(\frac 14\)(cosec \(\theta\) + cot \(\theta\)) (On multiplying both sides by cosec \(\theta\) + cot \(\theta\)) = \(cosec^2\theta - cot^2\theta = \frac 14 \) (cosec \(\theta\) + cot \(\theta\)) (\(\because\) (a-b) (a+b) = \(a^2 - b^2\)) = \(\frac 14\) (cosec \(\theta\) + cot \(\theta\)) = 1 (\(\because\) \(cosec^2\theta - cot^2\theta = 1\)) = cosec \(\theta\) + cot \(\theta\) = 4 Correct option is: D) 4

If Cosec θ – Cot θ = 1/4 then the value of Cosec θ + Cot θ isA) 1 B) -1 C) 1/4 D) 4

Answer»

Correct option is: D) 4

Given that Cosec \(\theta\) – Cot \(\theta\) = \(\frac 14\) ...(1)

\(\therefore\) ( cosec \(\theta\) - cot \(\theta\)) (cosec \(\theta\) + cot \(\theta\)) = \(\frac 14\)(cosec \(\theta\) + cot \(\theta\))

(On multiplying both sides by cosec \(\theta\) + cot \(\theta\))

= \(cosec^2\theta - cot^2\theta = \frac 14 \) (cosec \(\theta\) + cot \(\theta\)) (\(\because\) (a-b) (a+b) = \(a^2 - b^2\))

= \(\frac 14\) (cosec \(\theta\) + cot \(\theta\)) = 1 (\(\because\) \(cosec^2\theta - cot^2\theta = 1\))

= cosec \(\theta\) + cot \(\theta\) = 4

Correct option is: D) 4