which of the following is correct ?

To find the value of (tan²θ + 5) / (tan²θ - 5), we first determine the value of tanθ using the given equation:

(7sinθ + 4cosθ) / (9sinθ - 2cosθ) = 5 / 4

Step-by-Step Solution
Cross-multiply to solve for the relationship between sinθ and cosθ:
4 * (7sinθ + 4cosθ) = 5 * (9sinθ - 2cosθ)
28sinθ + 16cosθ = 45sinθ - 10cosθ

Rearrange the terms to group sinθ and cosθ:
16cosθ + 10cosθ = 45sinθ - 28sinθ
26cosθ = 17sinθ

Find the value of tanθ:
Since tanθ = sinθ / cosθ:
sinθ / cosθ = 26 / 17
tanθ = 26 / 17

Calculate tan²θ:
tan²θ = (26 / 17)² = 676 / 289

Substitute tan²θ into the expression (tan²θ + 5) / (tan²θ - 5):
Expression = [(676 / 289) + 5] / [(676 / 289) - 5]
Multiply numerator and denominator by 289:
Expression = (676 + 5 * 289) / (676 - 5 * 289)
Expression = (676 + 1445) / (676 - 1445)
Expression = 2121 / (-769)
Expression = -2121 / 769

Correct Option
Option B: -2121 / 769