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.

We'll write tan 2x as a sum of 2 like angles.

tan 2x = tan(x+x)

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

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

We know, from enunciation, that tan x= 1/7.

We'll substitute the value of tan x in the formula for tan 2x.

tan 2x = 2*(1/7)/(1 - 1/49)

tan 2x = (2/7)*(49/48)

We'll simplify:

tan 2x = 7/24

**tan 2x = 0.291(6)**