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

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ulichh | Student, College Freshman | (Level 1) Honors

Posted May 31, 2010 at 11:06 PM via web

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

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted May 31, 2010 at 11:08 PM (Answer #1)

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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

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hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted June 1, 2010 at 4:05 AM (Answer #2)

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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

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neela | High School Teacher | (Level 3) Valedictorian

Posted May 31, 2010 at 11:26 PM (Answer #3)

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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

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