If $tan a = \frac{2}{\sqrt{13}}$, then the value of $\frac{cosec^2a+2sec^2a}{cosec^2a-3sec^2a}$ is :

21

Given :- 

$tan a = \frac{2}{\sqrt{13}}$

{ tanθ = \(\frac{P }{B}\) }

P² + B² = H²

2² + (√13)² = H²

H² = 4 + 13 = 17

H = √17

Now,

$\frac{cosec^2a+2sec^2a}{cosec^2a-3sec^2a}$

= \(\frac{17/4 + 2 × 17/13 }{ 17/4 - 3× 17/13 }\)

= \(\frac{(221+136)/52 }{ (221-204)/52 }\)

= \(\frac{(357) }{ (17) }\)

= 21