Question

The expression the (-1 + tan x)/(1 + tan x) can be rewritten as which of the following?tan((3pi/4) - x)tan((5pi/4) - x)tan((3pi/4) + x)tan((5pi/4) + x)

Answer 1

To answer this question we need to remember the identity:

`\tan(A+B)=(\tan A+\tan B)/(1-\tan A\tan B)`

and that

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

If we let A be 3π/4 and B be x, we have:

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

Therefore, we have that:

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