If $tan a = \frac{2}{\sqrt{13}}$, then the value of $\frac{cosec^2a+2sec^2a}{cosec^2a-3sec^2a}$ is :
Answer & explanation
Correct answer: option 1
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