We can obtain a useful linear approximation of the function (x) = 1/(1 + tan x) at x = 0 by combining the approximations to

We can obtain a useful linear approximation of the function ƒ(x) = 1/(1 + tan x) at x = 0 by combining the approximations

to get

Show that this result is the standard linear approximation of 1/(1 + tan x) at x = 0.

1 1 + x 1 - x and tan x x