Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

`\tan(4x)`

Step-by-Step Explanation:

Notice that this resembles the difference identity for tangent. Specifically:

`\displaystyle \tan(\alpha-\beta)=(\tan(\alpha)-\tan(\beta))/(1+\tan(\alpha)\tan(\beta))`

So, given our equation, we can pretend that α=9x and β=5x. Therefore:

`\displaystyle (\tan(9x)-\tan(5x))/(1+\tan(9x)\tan(5x))=\tan(9x-5x)=\tan(4x)`

Answer 2

Answer: tan(14x)

Explanation:

Consider the Sum Formula for tan:

`tan(A + B)=(tan(A)+tan(B))/(1-tan(A)(tan(B))\\\\\\tan(9x+5x)=(tan(9x)+tan(5x))/(1-tan(9x)(tan(5x))\\\\\\\large\boxed{tan(14x)}=(tan(9x)+tan(5x))/(1-tan(9x)(tan(5x))`