Question

Solve the following equations.
$tan(x+\frac{\pi }{4})=?$

• A. $\frac{1+\tan x}{1-\tan x}$
• B. $\frac{1+\tan x}{1}$
• C. $\frac{1+\cos x}{2}$
• D. $\cos x$

Answer 1

The correct option is A $\frac{1+\tan x}{1-\tan x}$

We know,

$\tan (A+B)=\frac{\tan A+\tan B}{1-\tan A\tan B}$

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

$=\frac{1+\tan x}{1-\tan x}$