Functional Trigonometry

Geometry Level 3

$\large f(\theta)=\dfrac{(\cot^2\theta+5)(\cot^2\theta+10)}{\cot^2\theta+1}$

Find the range of $f(\theta)$ for all real values of $\theta$ .

None of the given.

[19,\infty)

[15,\infty)

[25,\infty)

[38,\infty)