Prove that tan(π/4 + x) = (1 + tan x)/(1 - tan x)…

Step 1. The identity. $\tan\left(\dfrac{\pi}{4} + x\right) = \dfrac{\tan \frac{\pi}{4} + \tan x}{1 - \tan \frac{\pi}{4} \tan x} = \dfrac{1 + \tan x}{1 - \tan x}$.

Step 2. Put $x = 30^\circ$. $\tan 75^\circ = \dfrac{1 + \frac{1}{\sqrt{3}}}{1 - \frac{1}{\sqrt{3}}} = \dfrac{\sqrt{3} + 1}{\sqrt{3} - 1}$.

Step 3. Simplify. Multiply the top and the bottom by $\sqrt{3} + 1$: $\dfrac{(\sqrt{3} + 1)^2}{2} = \dfrac{4 + 2\sqrt{3}}{2} = 2 + \sqrt{3} \approx 3.732$.