Derive the following identity: tan &#x2061;<!-- ⁡ --> ( 3 x ) = 3

Camille Flynn

Camille Flynn

Answered question

2022-05-20

Derive the following identity:
tan ( 3 x ) = 3 tan ( x ) tan 3 ( x ) 1 3 tan 2 ( x )

Answer & Explanation

Kaylyn Ewing

Kaylyn Ewing

Beginner2022-05-21Added 9 answers

MathJax(?): Can't find handler for document MathJax(?): Can't find handler for document We have
cos 3 x + i sin 3 x = cos 3 x + 3 i cos 2 x sin x 3 cos x sin 2 x i sin 3 x
so
sin 3 x = 3 cos 2 x sin x sin 3 x cos 3 x = cos 3 x 3 cos x sin 2 x tan 3 x = 3 cos 2 x sin x sin 3 x cos 3 x 3 cos x sin 2 x Now divide numerator and denominator by cos 3 x
Zeihergp

Zeihergp

Beginner2022-05-22Added 6 answers

Wthout de Moivre:
tan ( 2 x + x ) = tan 2 x + tan x 1 tan 2 x tan x = 2 tan x 1 tan 2 x + tan x 1 2 tan x 1 tan 2 x tan x =
= 3 tan x tan 3 x 1 3 tan 2 x = tan x ( tan x 3 ) ( tan x + 3 ) ( 3 tan x 1 ) ( 3 tan x + 1 )

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?