If $3(sec^2\theta + tan^2 \theta)= 5, 0° < \theta < 90°, $ then the value of cosec θ is :

$\frac{1}{\sqrt{3}}$ $\frac{2\sqrt{3}}{3}$ 2 $\frac{1}{2}$

2

3( sec²θ + tan²θ ) = 5    ----(1) We know, sec²θ - tan²θ = 1 Multiply this equation with 3 and add into equation 1. 6 sec²θ = 8  secθ = \(\frac{2}{√3}\) { we know,  sec30º = \(\frac{2}{√3}\) } so, θ = 30º Now, cosecθ = cosec 30º = 2