# Knowing tgx=4 calculate tg2x.

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The expansion for tan 2x = 2*tan x/(1 - (tan x)^2)

It is given that tan x = 4.

tan 2x = 2*tan x/(1 - (tan x)^2)

=> 2*4/(1 - 4^2)

=> 8/(1 - 16)

=> 8/-15

=> -8/15

**The required value of tan 2x = -8/15**

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.**