Question

How do you prove the identity `tan (x-pi/4)= (tan x - 1)/(1 + tan x)`?

Answer 1

The formula of difference of the tangent is:

`tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta)`,

so, in our case:

`tan(x-pi/4)=(tanx-tan(pi/4))/(1+tanxtan(pi/4))=(tanx-1)/(1+tanx)`

and this is because `tan(pi/4)=1`.