How to prove tan A = 2 tan B + cot B

Thanks for the help in advance.

This question can only be answered if more information is given, like a diagram, or relationship between A & B, like A+B=90^0.

Arun, I don’t have additional information. The textbook I’m referring to uses the relationship as a given, which is baffling to me.

Dear Achal,

        Then I am sorry, because as far as I know it would not be possible to solve the question. But, if you can say which textbook you are referring to, then maybe I may be of help.
 

Thanks, Arun.

 

If you google "2 tan b + cot b" the very first link is JEE Main Mathematics by Prem Kumar, and clicking that link will bring you to the problem.

 

The other book is Mathematics for Class XI by R.D. Sharma. In there is a problem that starts off as “given tan A = 2 tan B + cot B”

 

Seem like this a formula that is generally used and that I should be knowing.

 

 

Dear Achal,

        Very sorry, for at first I thought you were a 10^th grader. As I am one, I thought simple maths would help. But considering the fact that you are an 11^th grader, there does exist a few formulae which I looked up in my school library. I do not remember which month’s edition, but the magazine in which I came across this formula was named “Mathematics Today”. I will let you know the answer by Monday or Tuesday beacuse my school has closed for Muharrum and Vijayadasami.

Dear Achal,

       The identity is

tan(A-B)=(tan A – tan B) / (1+ tan A . tan B).

 With this, one would be able to find the answer.

Thanks for all the help, Arun. I’ll give your suggestion a try and see if it can get me where I want to go.