Simplify the expression algebraically. $4 \tan \left( \frac { \pi } { 4 } - \theta \right)$
A) $\frac { 4 - 4 \tan \theta } { 1 + \tan \theta }$
B) $\frac { 4 - 4 \tan \theta } { \tan \theta }$
C) $\frac { \tan \theta } { 4 - \tan \theta }$
D) $\frac { 4 + 4 \tan \theta } { 1 - \tan \theta }$
E) $\frac { 4 + 4 \tan \theta } { \tan \theta }$

Question

Simplify the expression algebraically. $4 \tan \left( \frac { \pi } { 4 } - \theta \right)$  
A) $\frac { 4 - 4 \tan \theta } { 1 + \tan \theta }$
B) $\frac { 4 - 4 \tan \theta } { \tan \theta }$
C) $\frac { \tan \theta } { 4 - \tan \theta }$
D) $\frac { 4 + 4 \tan \theta } { 1 - \tan \theta }$
E) $\frac { 4 + 4 \tan \theta } { \tan \theta }$

Quizplus · Accepted Answer

Using the tangent subtraction formula, $\tan(a - b) = \frac{\tan a - \tan b}{1 + \tan a \tan b}$, with $a = \frac{\pi}{4}$ and $b = \theta$, and knowing that $\tan(\frac{\pi}{4}) = 1$, we get $\tan(\frac{\pi}{4} - \theta) = \frac{1 - \tan \theta}{1 + \tan \theta}$. Multiplying by 4 gives the expression $\frac{4 - 4\tan \theta}{1 + \tan \theta}$.

Simplify the Expression Algebraically 4tan⁡(π4−θ)4 \tan \left( \frac { \pi } { 4 } - \theta \right)4tan(4π​−θ)

Simplify the Expression Algebraically $4 \tan \left( \frac { \pi } { 4 } - \theta \right)$