## anonymous one year ago 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

1. freckles

try using the sum formula identity for tan

2. freckles

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

3. anonymous

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

4. freckles

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

5. freckles

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

6. anonymous

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

7. freckles

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

8. freckles

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

9. freckles

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

10. anonymous

ok i did that now what

11. freckles

what did you get for the thing in red?

12. freckles

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

13. anonymous

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

14. freckles

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

15. freckles

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

16. freckles

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

17. freckles

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

18. anonymous

ok so how do i get rid of the extra fractions

19. freckles

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

20. anonymous

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

21. freckles

you left a term out on top

22. freckles

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

23. anonymous

24. anonymous

Thx a ton for all the help!!!

25. freckles

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

26. freckles

and yes you get a as a result