If $$\cos \theta = \frac{2p}{p^2 + 1}$$, (p ≠ 0) then $$\tan \theta$$ is equal to:

$$\cos \theta = \frac{2p}{p^2 + 1}$$ .

We know $$\cos \theta$$ symbolises base and Hypotenuse in ratio format.

Similarly, $$\tan \theta$$ symbolises perpendicular and base in ratio format .

So we have to find the perpendicular, whose base and hypotenuse are given,

Base= B = 2p wherease Hypotenuse = H=$$p^2 + 1$$

Therefore Perpendicular = P = $$\sqrt{H^2 - B^2}$$ = $$p^2 - 1$$

$$\tan \theta = P/B = \frac{p^2 - 1}{2p}$$