Question

If (cosec x + cot x)/(cosec x – cot x) = 7. Then, find the value of (4sin²x + 1)/(4sin²x – 1).
1. 12/11
2. 11/3
3. 13/5
4. 12/7

Answer 1

Correct Answer - Option 2 : 11/3

Given

(cosec x + cot x)/(cosec x – cot x) = 7

Formula used

Cos²x = 1 – sin²x

Calculation

(cosec x + cot x)/(cosec x – cot x) = 7

⇒ (cosec x + cot x = 7(cosec x – cot x)

⇒ 8cot x = 6 cosec x

⇒ (8cos x)/sin x = 6/sin x

⇒ Cos x = 3/4

⇒ Cos² x = 9/16

⇒ Sin² x = 1 – 9/16

⇒ Sin² x = 7/16

⇒ (4sin2x + 1)/(4sin2x – 1) = (4 × 7/16 + 1)/(4 × 7/16 – 1)

⇒ (7/4 + 1)/(7/4 –1)

⇒ (11/4)/(3/4)

⇒ 11/3

∴ The value of  (4sin2x + 1)/(4sin2x – 1) is 11/3