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

The expression can be simplified using the tangent subtraction formula: $\tan(A - B) = \frac{\tan A - \tan B}{1 + \tan A \tan B}$. Here, $A = \frac{\pi}{4}$ and $B = \theta$, so $\tan\left(\frac{\pi}{4} - \theta\right) = \frac{\tan\left(\frac{\pi}{4}\right) - \tan(\theta)}{1 + \tan\left(\frac{\pi}{4}\right)\tan(\theta)}$. Since $\tan\left(\frac{\pi}{4}\right) = 1$, the expression simplifies to $\frac{1 - \tan(\theta)}{1 + \tan(\theta)}$. Multiplying by 4 gives $\frac{4 - 4\tan(\theta)}{1 + \tan(\theta)}$.

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

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