θ and φ are complementary angles. tan θ = 0.5 What is tan φ?

Since $\theta$ and $\varphi$ are complementary, then $\theta + \varphi = 90^\circ$

Therefore, $\varphi = 90^\circ - \theta$

So,

$\tan \varphi = \dfrac{ \sin \varphi }{\cos \varphi} = \dfrac{ \sin(90^\circ - \theta) }{\cos(90^\circ - \theta) } = \dfrac{ \cos \theta }{\sin \theta} = \cot \theta = \dfrac{1}{\tan \theta}$

Therefore, $\tan \varphi = \dfrac{1}{0.5} = 2$