Join TSR now and get all your revision questions answeredSign up now

C2 maths help Watch

    • Thread Starter
    Offline

    2
    ReputationRep:
    show that (2 - cos^2 x) / (1 + sin^2 x) is equal to 1

    I have substituted cos^2 x by (1 - sin^2 x) but I don't know what to do next
    Offline

    1
    ReputationRep:
    what past paper is this from?
    Offline

    0
    ReputationRep:
    (Original post by man111111)
    show that (2 - cos^2 x) / (1 + sin^2 x) is equal to 1

    I have substituted cos^2 x by (1 - sin^2 x) but I don't know what to do next
    Hi,

    I did for LHS:

    (2 - cos^2 x) / (1+ 1 - cos^2 x)

    So, (2 - cos^2 x) / ( 2 - cos ^2 x)

    which equals 1

    If you substitute cos^2 x by (1 - sin^2 x):

    [ 2 - (1 - sin^2 x)] / (1 + sin^2 x)

    So, ( 1 + sin^2 x ) / (1+ sin^2 x )
    • Thread Starter
    Offline

    2
    ReputationRep:
    (Original post by XavierD)
    Hi,

    I did for LHS:

    (2 - cos^2 x) / (1+ 1 - cos^2 x)

    So, (2 - cos^2 x) / ( 2 - cos ^2 x)

    which equals 1

    If you substitute cos^2 x by (1 - sin^2 x):

    [ 2 - (1 - sin^2 x)] / (1 + sin^2 x)

    So, ( 1 + sin^2 x ) / (1+ sin^2 x )
    hi thanks for replying,
    I don't understand why [2 - (1 - sin^2 x)] gives you 1+sin^2x

    In addition, I don't understand why [1+ (1 - cos^2 x)] gives you 2 - cos^2 x
    Offline

    3
    ReputationRep:
    u need the rule

    sin2x + cos2x = 1

    so we got
    2-cos2x / 1+ sin2x

    we can substitute cos2x with 1-sin2x so we would get

    2 - (1-sin2x)/1+sin2x {I think u forgot that u have to put brackets in}

    so we would then get

    2 - 1 + sin2x / 1 + sin2x

    which equals to

    1 + sin2x / 1 + sin2x

    which then equals to
    1

    I think u forgot the fact that you had to put the 1 - sin2x inside a bracket.
    Offline

    0
    ReputationRep:
    (Original post by man111111)
    hi thanks for replying,
    I don't understand why [2 - (1 - sin^2 x)] gives you 1+sin^2x

    In addition, I don't understand why [1+ (1 - cos^2 x)] gives you 2 - cos^2 x
    I just opened the brackets,

    for: 2 - ( 1 - sin^2 x)

    equals: 2 - 1 + sin^2 x

    so, 1 +sin^2 x

    for: 1 + ( 1 - cos^2 x)

    opening the brackets: 1 + 1 - cos^2 x

    so, 2 - cos^2 x

    Please let me know if this helps
 
 
 
Poll
Still A Remainer Or A Brexiteer?
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.