Join TSR now and get all your revision questions answeredSign up now
    • Thread Starter
    Offline

    0
    ReputationRep:
    Prove that 4(sin4x+cos4x) = cos4x+3

    Thanks
    Offline

    3
    ReputationRep:
    (Original post by Stokeesy)
    Prove that 4(sin4x+cos4x) = cos4x+3

    Thanks
    Writing cos2x and sin2x in terms of cos2x would be a good starting point.
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Mr Inquisitive)
    Writing cos2x and sin2x in terms of cos2x would be a good starting point.
    Not really got any where
    Offline

    3
    ReputationRep:
    (Original post by Stokeesy)
    Not really got any where
    What have you tried? Can you show your working out?
    • Thread Starter
    Offline

    0
    ReputationRep:
    (Original post by Mr Inquisitive)
    What have you tried? Can you show your working out?
    4(sin4x+cos4x)
    = 4sin4x+4cos4x
    = 2sin2x2sin2x+2cos2x2cos2x
    = (cos2x-1)(cos2x-1)+(cos2x+1)(cos2x+1)
    ......
    Offline

    16
    ReputationRep:
    (Original post by Stokeesy)
    4(sin4x+cos4x)
    = 4sin4x+4cos4x
    = 2sin2x2sin+2cos2x2cos2?x
    = (cos2x-1)(cos2x-1)+(cos2x+1)(cos2x+1)
    ......
    Try starting off by considering (cos^2{x}-sin^2{x})^2
    Offline

    3
    ReputationRep:
    (Original post by Stokeesy)
    4(sin4x+cos4x)
    = 4sin4x+4cos4x
    = 2sin2x2sin+2cos2x2cos2?x
    = (cos2x-1)(cos2x-1)+(cos2x+1)(cos2x+1)
    ......
    That method's quite messy, and seems to be riddled with mistakes.

    Take it one step at a time. First write sin2x and cos2x in terms of cos2x.

    We know that cos2x = cos2x - sin2x, so we can make deductions from that as to what they are.
 
 
 
Poll
Which Fantasy Franchise is the best?
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

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