Question

By first expanding tan(2x+x) , show that (3k-1)tan^2x=k-3

Answer 1

Answer:

A Start: As you know, you will need to use tan2x=2tanx1−tan2x and tan(x+2x)=tanx+tan2x1−tanxtan2x

If you do the expansion carefully, you will find that

tan3x=3tanx−tan3x1−3tan2x.

Set this equal to ktanx, and simplify a bit.

You will be able to "cancel" a tanx, if tanx≠0. (That condition was unfortunately left out in the statement of the problem.)

Then manipulation should get you to where you want to go.