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) $\tan ( x ) - 23 \pi$

Question

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) $\tan ( x ) - 23 \pi$

Quizplus · Accepted Answer

Since $\tan(x + y) = \frac{\sin(x + y)}{\cos(x + y)}$, and knowing that $\sin$ and $\cos$ functions are periodic with a period of $2\pi$, adding $23\pi$ to $x$ does not change the value of $\tan(x)$ because $23\pi$ is an odd multiple of $\pi$, making the tangent function return to its original value at $x$.

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

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