# Question 2533c

Feb 14, 2018

$- 1$

#### Explanation:

This is based on the double angle formula for $\tan x$

$\tan \left(2 x\right) = \frac{2 \tan x}{1 - {\tan}^{2} x}$

x, in your problem, is $\frac{7 \pi}{8}$, so your problem is really looking for :

$\tan \left(2 \left(\frac{7 \pi}{8}\right)\right) = \frac{2 \tan \left(\frac{7 \pi}{8}\right)}{1 - {\tan}^{2} \left(\frac{7 \pi}{8}\right)}$

$\tan \left(2 \left(\frac{7 \pi}{8}\right)\right) = \tan \left(\frac{14 \pi}{8}\right) = \tan \left(\frac{7 \pi}{4}\right)$

$\tan \left(\frac{7 \pi}{4}\right) = - 1$

Feb 14, 2018

See the explanation

#### Explanation:

 [2tan((7pi)/8)]/(1 - tan^2((7pi)/8)

It is in the form of

$\frac{2 \tan x}{1 - {\tan}^{2} x}$

Which is an identity and is equal to $\tan 2 x$.

So,  [2tan((7pi)/8)]/(1 - tan^2((7pi)/8)

$= \tan \left(2 \cdot \frac{7 \pi}{8}\right)$

$= \tan \left(\frac{7 \pi}{4}\right)$

Now put pi = 180°

We get , $\tan \left(7 \cdot \frac{180}{4}\right)$

$= \tan \left(7 \cdot 45\right)$

= tan (315°)

Now you can use the tables to find the value of tan (315°)# which is equal to -1.