Answer
$tan\theta= 2$,
$cot\theta= \frac{1}{2}$,
$sec\theta= \sqrt 5$,
$csc\theta= \frac{\sqrt 5}{2}$.
Work Step by Step
Given $sin\theta=\frac{2\sqrt 5}{5}, cos\theta=\frac{\sqrt 5}{5}$, we have:
$tan\theta=\frac{sin\theta}{cos\theta}=2$,
$cot\theta=\frac{cos\theta}{sin\theta}=\frac{1}{2}$,
$sec\theta=\frac{1}{cos\theta}=\sqrt 5$,
$csc\theta=\frac{1}{sin\theta}=\frac{\sqrt 5}{2}$.