Question

simplify the expression tan (3 x+ 2pi) as the tangent of a single angle

Answer 1

tan(3x)

Explanation

$\tan (3x+2\pi)$

Step 1

remember some property

$\tan (a+b)=\frac{\tan a+\tan b}{1-\tan a\tan b}$

then

$\begin{gathered} \tan (3x+2\pi)=\frac{\tan 3x+\tan 2\pi}{1-\tan 3x\tan 2\pi}\text{ Equation(1)} \\ \tan \text{ 2}\pi=0 \\ so \\ \tan (3x+2\pi)=\frac{\tan 3x+0}{1-\tan 3x\cdot0}\text{ } \\ \tan (3x+2\pi)=\frac{\tan \text{ 3x}}{1-0}=\frac{\tan \text{ 3x}}{1} \\ \tan (3x+2\pi)=\tan (3x) \end{gathered}$

I hope this helps you