Answer:
[tex]\tan(4x)[/tex]
Step-by-Step Explanation:
Notice that this resembles the difference identity for tangent. Specifically:
[tex]\displaystyle \tan(\alpha-\beta)=\frac{\tan(\alpha)-\tan(\beta)}{1+\tan(\alpha)\tan(\beta)}[/tex]
So, given our equation, we can pretend that α=9x and β=5x. Therefore:
[tex]\displaystyle \frac{\tan(9x)-\tan(5x)}{1+\tan(9x)\tan(5x)}=\tan(9x-5x)=\tan(4x)[/tex]
