Question

The equation tan(x+pi/6) is equal to _____.

a. √3 tanx+1/√3-tanx
b. tanx+√3/1-√3 tanx
c. tanx-√3/1+√3tanx
d. √3 tanx-1/√3+tanx

Answer 1

try using the sum formula identity for tan

Answer 2

\[\tan(a+b)=\frac{\tan(a)+\tan(b)}{1-\tan(a)\tan(b)}\]

Answer 3

I got (tan(x)+tan(pi/6))/1-tan(x)tan(pi/6) how does that help me?

Answer 4

do you know how to evaluate tan(pi/6)?

Answer 5

\[\tan(\frac{\pi}{6})=\frac{\sin(\frac{\pi}{6})}{\cos(\frac{\pi}{6})}=....\]

Answer 6

but the equation is tan(x+pi/6) so how does that work

Answer 7

so when you used the sum identity just a sec ago
you don't see tan(pi/6)?

Answer 8

I'm asking you to evaluate tan(pi/6)

Answer 9

\[\tan(x+\frac{\pi}{6})=\frac{\tan(x)+\color{red}{\tan(\frac{\pi}{6})}}{1-\tan(x) \color{red}{\tan(\frac{\pi}{6})}}\]
I'm asking you to evaluate this thing in red

Answer 10

ok i did that now what

Answer 11

what did you get for the thing in red?

Answer 12

the unit circle says tan(pi/6) is..

Answer 13

(so i got tan(x)+rt(3))/(1-tan(x)rt(3))

Answer 14

hmm shouldn't tan(pi/6) be 1/sqrt(3)?

Answer 15

\[\tan(\frac{\pi}{6})=\frac{\sin(\frac{\pi}{6})}{\cos(\frac{\pi}{6})}=\frac{\frac{1}{2}}{\frac{\sqrt{3}}{2}}=\frac{1}{\sqrt{3}}\]

Answer 16

\[\tan(x+\frac{\pi}{6})=\frac{\tan(x)+\color{red}{\frac{1}{\sqrt{3}}}}{1-\tan(x) \color{red}{\frac{1}{\sqrt{3}}}}\]

Answer 17

multiply top and bottom of the big fraction by sqrt(3)

Answer 18

ok so how do i get rid of the extra fractions

Answer 19

multiply top and bottom of the big fraction by sqrt(3)

Answer 20

so (rt(3)tan(x))/(rt(3)-tanx)

Answer 21

you left a term out on top

Answer 22

sqrt(3)/sqrt(3) isn't 0

Answer 23

so the answer is a

Answer 24

Thx a ton for all the help!!!

Answer 25

\[\tan(x+\frac{\pi}{6})=\frac{\tan(x)+\color{red}{\frac{1}{\sqrt{3}}}}{1-\tan(x) \color{red}{\frac{1}{\sqrt{3}}}} \cdot \frac{\color{blue}{\sqrt{3}}}{ \color{blue}{\sqrt{3}}} \\ \tan(x+\frac{\pi}{6})= \frac{\color{blue}{\sqrt{3}} \tan(x)+\frac{\color{blue }{\sqrt{3}}}{\color{red}{\sqrt{3}}}}{\color{blue}{\sqrt{3}}-\tan(x) \frac{\color{blue}{\sqrt{3}}}{\color{red}{\sqrt{3}}}} \]

Answer 26

and yes you get a as a result