Question

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

Answer 1

tan(3x)

Step-by-step explanation

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

Step 1

remember some property

`\tan (a+b)=(\tan a+\tan b)/(1-\tan a\tan b)`

then

`\begin{gathered} \tan (3x+2\pi)=(\tan 3x+\tan 2\pi)/(1-\tan 3x\tan 2\pi)\text{ Equation(1)} \\ \tan \text{ 2}\pi=0 \\ so \\ \tan (3x+2\pi)=(\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