anonymous 3 years ago Rewrite the expression as a trigonometric function of a single angle measure.

1. anonymous

$\frac{ \tan4 \theta + \tan 2 \theta }{ 1 - \tan 4 \theta + \tan 2 \theta }$

2. anonymous

hi. do you still need help with this one?

3. anonymous

Yes, I'm so lost on how to solve it

4. anonymous

do you know the tangent addition formula?

5. anonymous

tan(a+b)=(tan a +tan b)/(1-tan a tanb)

6. anonymous

have you seen this formula before?

7. anonymous

now think about the angle a=4theta and the angle b=2theta. does this help?

8. anonymous

Ive seen it but never used it,

9. anonymous

ah. well, your teacher is giving you the opportunity here

10. anonymous

I'm confused on how I solve it with the this formula using the 'theta'

11. anonymous

ok. well, it is more recognition than solving. look at the form of the equation i gave you and the relation you wrote above. write this puppy as the tangent of the sum of the two angles you have been given (4theta and 2theta)

12. anonymous

it is good to ask questions if you are in doubt. :)

13. anonymous

Sorry, If it takes to long to respond, I'm still confused a little so I'm trying to write it down so that would hopefully help me get it

14. anonymous

no problem. so the form of the equation is tan (a+b)=(tan a +tan b)/(1-tan a tan b). substitute for a 4theta and for b 2theta

15. anonymous

So, tan 4theta + tan 2theta / 1- tan 4theta * tan 2.?

16. anonymous

we are interested in the left side. the tan (a+b) part. this condenses the mess you were given.

17. anonymous

So 4 theta + 2 theta.?

18. anonymous

which becomes tan ?

19. anonymous

You would add the 4 & 2 together & get 6 & 6 would be the tan wouldn't it.?

20. anonymous

perfect. yes!! so you tan 6theta, which is the trig function (tan) of a single angle 6theta.

21. anonymous

Alright thank you for help.! :-) I understand this now.!