Question

The expression the quantity 1 plus tangent x end quantity over the quantity 1 minus tangent x end quantity can be rewritten as which of the following

Answer 1

The identity for a tangent of the subtraction of two angles is:

`\tan (\theta-x)=(\tan(\theta)-\tan(x))/(1+\tan(\theta)\cdot\tan(x))=(-\tan(\theta)+\tan(x))/(-1-\tan(\theta)\cdot\tan(x))`

Then, given the expression:

`(1+\tan(x))/(-1+\tan(x))`

We identify:

`\begin{gathered} \tan (\theta)=-1 \\ \Rightarrow\theta=(3\pi)/(4) \end{gathered}`

We conclude that:

`(1+\tan(x))/(-1+\tan(x))=\tan ((3\pi)/(4)-x)`