# Calculate tg 2x , if tg x = 1/3 .

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If tg(x)=1/3 , find tg(2x)

We know that: tg(2x)= 2 tg(x)/[1-(tgx)^2

==> tg(2x) = 2(1/3)/[1-(1/3)^2]

= (2/3)/[1-1/9]

=(2/3)/(8/9)

= 2*9/3*8 = 18/24 = 3/4

To calculate tg 2x, we'll consider 2x as a sum of 2 identical angles.

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

tg 2x=2tg x/[1-(tgx)^2]

We know, from enunciation, that tg x= 1/3.

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

tg 2x = 2*1/3/(1 - 1/9)

tg 2x = (2/3)*(9/8)

**tg 2x =3/4**

tanx = 1/3. To find tan2x.

We know that tan2x = 2tanx/(1-(tanx)^2) = 2*(1/3)/(1-(1/3)^2) = (2/3) / {1-1/9) = (2/3)/(8/9) = 2*9/(3*8) = 3/4