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

    2
    ReputationRep:
    Show that 2Sin2X - 3Cos2X - 3SinX + 3 = SinX(4CosX+6SinX - 3)

    hmm.. Where do I start?

    I'd appreciate any help

    Thanks.
    Offline

    17
    ReputationRep:
    (Original post by Jonario)
    Show that 2Sin2X - 3Cos2X - 3SinX + 3 = SinX(4CosX+6SinX - 3)

    hmm.. Where do I start?

    I'd appreciate any help

    Thanks.
    Multiply out the RHS and note that \sin 2x = 2\sin x \cos x and \cos 2x= 1-2\sin ^2x.
    • Community Assistant
    Offline

    19
    ReputationRep:
    (Original post by Jonario)
    Show that 2Sin2X - 3Cos2X - 3SinX + 3 = SinX(4CosX+6SinX - 3)

    hmm.. Where do I start?

    I'd appreciate any help

    Thanks.
    Presumably you know the double angles identities for sin 2x and cos 2x?
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Farhan.Hanif93)
    Multiply out the RHS and note that \sin 2x = 2\sin x \cos x and \cos 2x= 1-2\sin ^2x.
    I got 4cosXSinX+6sin^2X - 3sinX

    but you see when you say note.. Does that mean I have to rearrange the LHS?
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Mr M)
    Presumably you know the double angles identities for sin 2x and cos 2x?
    Yes I do

    2 Sin 2X = 2Sin2XCos2X?
    Offline

    0
    ReputationRep:
    (Original post by Jonario)
    Yes I do

    2 Sin 2X = 2Sin2XCos2X?
    No need for that first 2 and the 2X is just X on the RHS.
    Offline

    0
    ReputationRep:
    (Original post by Jonario)
    Yes I do

    2 Sin 2X = 2Sin2XCos2X?
    If this were true cos(2x)=1.....always.:eek:
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Yellowmonkeyman)
    No need for that first 2 and the 2X is just X on the RHS.
    Oh man i'm so confused now.

    Do I start with the RHS or the LHS, do i even change the LHS?
    Offline

    17
    ReputationRep:
    (Original post by Jonario)
    Oh man i'm so confused now.

    Do I start with the RHS or the LHS, do i even change the LHS?
    No. What you do here is take ONE side of the equation and make it look the same as the other without changing the other side itself. You need to do this using identities.
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Farhan.Hanif93)
    No. What you do here is take ONE side of the equation and make it look the same as the other without changing the other side itself. You need to do this using identities.
    Ok so i get the RHS SinX(4cosX+6SinX-3) and multiply out.

    I get 4cosXSinX+6Sin^2X - 3Sinx

    Then I use the double angle formulae .. but I can't point out which one I use
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Farhan.Hanif93)
    No. What you do here is take ONE side of the equation and make it look the same as the other without changing the other side itself. You need to do this using identities.
    The LHS has 2sin2X so I use the SIN2A formulea? but how do I convert the RHS to this?
    Offline

    17
    ReputationRep:
    (Original post by Jonario)
    Ok so i get the RHS SinX(4cosX+6SinX-3) and multiply out.

    I get 4cosXSinX+6Sin^2X - 3Sinx

    Then I use the double angle formulae .. but I can't point out which one I use
    Well I've told you that \sin 2x =2\sin x \cos x. If you notice that 4\cos x \sin x = 2 \times 2\sin x \cos x. What is that equal to?
    Also do you agree that 4\sin x \cos x + 6\sin ^2x - 3 + 3 - 3\sin x is equal to what you got when you expanded out the RHS?
    Then perhaps notice that 6\sin ^2x - 3 = -(3-6\sin ^2x) = -3 \times (1-2\sin ^2x).
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by Farhan.Hanif93)
    Well I've told you that \sin 2x =2\sin x \cos x. If you notice that 4\cos x \sin x = 2 \times 2\sin x \cos x. What is that equal to?
    Also do you agree that 4\sin x \cos x + 6\sin ^2x - 3 + 3 - 3\sin x is equal to what you got when you expanded out the RHS?
    Then perhaps notice that 6\sin ^2x - 3 = -(3-6\sin ^2x) = -3 \times (1-2\sin ^2x).
    4\cos x \sin x = 2 \times 2\sin x \cos x
    How Is that true?
    Offline

    17
    ReputationRep:
    (Original post by Jonario)
    4\cos x \sin x = 2 \times 2\sin x \cos x
    How Is that true?
    Of course that's true, that's simple multiplication. No trig identities involved at all. if you have 4 apples, thats the same as having 2 lots of two apples.
    Offline

    0
    ReputationRep:
    (Original post by Jonario)
    4\cos x \sin x = 2 \times 2\sin x \cos x
    How Is that true?
    err...because 2*2=4 and sinx*cosx=cosx*sinx or did you mean something else?

    (note that I've used the star* as the sign for multiplication)
    Offline

    14
    ReputationRep:
    2sin2x = 4sinxcosx
    cos2x= 1- sin^2 x

    now expand:
    4sinxcosx-3+6sin^2 x -3sinx +3
    .... and factorise
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
    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
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • 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

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