Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 227: 40

$$\tan(\frac{\pi}{4}+x)=\frac{1+\tan x}{1-\tan x}$$

$$\tan(\frac{\pi}{4}+x)$$ Apply the identity of tangent of a sum here, we have $$=\frac{\tan\frac{\pi}{4}+\tan x}{1-\tan\frac{\pi}{4}\tan x}$$ $$=\frac{1+\tan x}{1-1\times \tan x}$$ $$=\frac{1+\tan x}{1-\tan x}$$