Knowing tgx=4 calculate tg2x.

This problem requires the use of the double angle
identity:

tan 2x = tan (x+x) = (tan x + tan x)/[1 - (tan
x)^2]

We'll replace tan x by the given value
4:

tan 2x = (4+4)/(1 - 16)

tan
2x = 8/(-15)

tan 2x =
-8/15

The requested value of tan2x, if tan x
= 4, is tan 2x = -8/15.