If 9sinθ = 4cosθ; then value of

\(\frac{cosec^2 θ + sec^2 θ}{cosec^2 θ - sec^2 θ}\) is:

\(\frac{97}{65}\)

9sinθ = 4cosθ ⇒ tanθ = \(\frac{4}{9}\)

cotθ = \(\frac{9}{4}\)

\(\frac{cosec^2θ + sec^2 θ}{cosec^2 θ - sec^2 θ}\) ⇒ \(\frac{sec^2 θ(cot^2 θ + 1)}{sec^2 θ (cot^2 θ - 1)}\)

=\(\frac{(\frac{9}{4})^2 + 1 }{(\frac{9}{4})^2 - 1}\) 

=\(\frac{\frac{81}{16} + 1}{\frac{81}{16} - 1}\)

=\(\frac{\frac{97}{16}}{\frac{65}{16}}\)

=\(\frac{97}{65}\)