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

hi. do you still need help with this one?

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

do you know the tangent addition formula?

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

have you seen this formula before?

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

Ive seen it but never used it,

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

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

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

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

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

So 4 theta + 2 theta.?

which becomes tan ?

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

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

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