Question

Rewrite the expression as a trigonometric function of a single angle measure.

Answer 1

\[\frac{ \tan4 \theta + \tan2 \theta }{ 1-\tan4\theta \tan2\theta } \]

Answer 2

without knowing the answer exactly, i am going to guess that it is \(\tan(6\theta)\)

Answer 3

a. tan6 theta
b. cot6 theta
c. tan4 theta
d. cot4 theta

Answer 4

and here is the reason for my guess.

look up the "addition angle formula" for \(\tan(\alpha +\beta)\)

Answer 5

if it is
\[\tan(\alpha +\beta)=\frac{\tan(\alpha)+\tan(\beta)}{1-\tan(\alpha)\tan(\beta)}\]
then imagine \(\alpha =4\theta\) and \(\beta=2\theta\) and you get it right away

Answer 6

if it is not , then i am wrong.

Answer 7

ok it is correct. i just checked

Answer 8

thank you so much!

Answer 9

yw