Use the Addition Formulas To Express $\tan ( x + 23 \pi )$

Use the addition formulas: $$\begin{array} { l } \sin ( x + y ) = \sin x \cdot \cos y + \cos x \cdot \sin y \\\sin ( x - y ) = \sin x \cdot \cos y - \cos x \cdot \sin y \\\cos ( x + y ) = \cos x \cdot \cos y - \sin x \cdot \sin y \\\cos ( x - y ) = \cos x \cdot \cos y + \sin x \cdot \sin y\end{array}$$
To express $\tan ( x + 23 \pi )$ in terms of $\tan ( x )$ .

A) $\frac { \tan ( x ) } { 23 \pi }$
B) $\tan ( x ) + 23 \pi$
C) $23 \pi \tan ( x )$
D) $\tan ( x )$
E) $\tan ( x ) - 23 \pi$

Correct Answer:

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