Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    17
    ReputationRep:
    I don't know where to start.

    

Use De Moivre's Theorem to show that

\tan 3\theta = \frac{ 3\tan \theta - \tan^3 \theta }{ 1 - 3 \tan^2 \theta }

    Sorry, I'm just really stupid today (if not every day).
    Offline

    19
    ReputationRep:
    (Original post by StarvingAutist)
    I don't know where to start.

    

Use De Moivre's Theorem to show that

\tan 3\theta = \frac{ 3\tan \theta - \tan^3 \theta }{ 1 - 3 \tan^2 \theta }

    Sorry, I'm just really stupid today (if not every day).



    http://madasmaths.com/archive/maths_..._questions.pdf

    look at Q96 how to do tan4θ and adapt it
    Offline

    15
    ReputationRep:
    you know by De Moivre that:

    (\cos(x)+i \sin(x))^{3} = \cos(3x)+i \sin(3x)

    1) Expand the left side (as a binomial expansion)

    you get, after sorting into real and imaginary parts:

    (\cos^{3}(x)-3 \cos(x) \sin^{2}(x))+i \times (3 \cos^{2}(x) \sin(x) - \sin^{3}(x))

    these correspond to the real/imaginary parts of the right-hand-side.

    Divide the imaginary part by the real part (and you have sin(3x)/cos(3x) = tan(3x) (at least on the lhs)

    then divide the top and bottom of the fraction you get by  \cos^{3}(x)

    (this doesn`t alter it , if you times top and bottom by same thing)
    • Thread Starter
    Offline

    17
    ReputationRep:
    (Original post by TeeEm)
    http://madasmaths.com/archive/maths_..._questions.pdf

    look at Q96 how to do tan4θ and adapt it
    Ah I see, thanks
 
 
 
Poll
Do you agree with the PM's proposal to cut tuition fees for some courses?
Useful resources

Make your revision easier

Maths

Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

Equations

How to use LaTex

Writing equations the easy way

Student revising

Study habits of A* students

Top tips from students who have already aced their exams

Study Planner

Create your own Study Planner

Never miss a deadline again

Polling station sign

Thinking about a maths degree?

Chat with other maths applicants

Can you help? Study help unanswered threads

Groups associated with this forum:

View associated groups

The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

Write a reply...
Reply
Hide
Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.