What is tan 2x if tan x = 1/7 ?

tanx = 1/7. To find tan2x
.

We  express tan2x , in terms of tanx and , then
substitute the given value of x to get tan2x.

We know that
tan(a+b) = (tanA +tanB)/{1-tanA*tanB}

Put A = B=
x.

Then tan2x = tan(x+x) =
(tanx+tanx)/(1-tanx*tanx)

Therefore tan2x =
2tanx/{1-(tanx)^2}..(1)

Now we substitute tanx = 1/7 in 
eq(1):

tan2x =
2(1/7)/{1-(1/7)^2}

Multiply both numerator and denominator
by 49:

tan2x =
2*7/{49-1}

tan2x = 14/48

tan2x
= 7/24.