Hey there! Sign in to join this conversationNew here? Join for free
Turn on thread page Beta
    • Thread Starter
    Offline

    10
    ReputationRep:
    Why do they just completely ignore the denominator? They replace 2sin^2x with 2(1-cos^2x) but they seem to ignore the sinxcosx denominator? Why is this? I'm really confused.

    Name:  Screenshot_101.png
Views: 25
Size:  153.8 KB
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by vector12)
    Why do they just completely ignore the denominator? They replace 2sin^2x with 2(1-cos^2x) but they seem to ignore the sinxcosx denominator? Why is this? I'm really confused.
    The denom isn't very useful and can be cancelled.
    Offline

    6
    ReputationRep:
    (Original post by vector12)
    Why do they just completely ignore the denominator? They replace 2sin^2x with 2(1-cos^2x) but they seem to ignore the sinxcosx denominator? Why is this? I'm really confused.

    Name:  Screenshot_101.png
Views: 25
Size:  153.8 KB
    Think of it as if the denominators where just numbers...
    if you had an expression over 5 equal to another expression over 5 you would just cancel them both so because t makes no difference, you can do the same thing here

    if you multiply both sides by the denominator then it disappears which is essentially what they've done
    • Thread Starter
    Offline

    10
    ReputationRep:
    (Original post by Canine Copycat)
    Think of it as if the denominators where just numbers...
    if you had an expression over 5 equal to another expression over 5 you would just cancel them both so because t makes no difference, you can do the same thing here

    if you multiply both sides by the denominator then it disappears which is essentially what they've done
    That makes sense when you think of it like that involving an equals sign, like 2/5 = x/5, then x=5.

    However, I did it like this where I moved it all to the LHS and made it equal to 0, which doesn't seem right to cancel the denominator that way, since you can only do it if something equals something else, over the same denominator. I guess I just needed to realise that when they were equal, i could cancel the denominator?

    Name:  unnamed (44).jpg
Views: 27
Size:  494.3 KB
    • Community Assistant
    Online

    20
    ReputationRep:
    Community Assistant
    (Original post by vector12)
    That makes sense when you think of it like that involving an equals sign, like 2/5 = x/5, then x=5.

    However, I did it like this where I moved it all to the LHS and made it equal to 0, which doesn't seem right to cancel the denominator that way, since you can only do it if something equals something else, over the same denominator. I guess I just needed to realise that when they were equal, i could cancel the denominator?
    You just need to realise that \displaystyle \frac{f(x)}{h(x)}=\frac{g(x)}{h(  x)} \Rightarrow f(x)=g(x) by simply multiplying both sides of the equation by h(x).

    Or, like you did, get \frac{f(x)-g(x)}{h(x)}=0 and then mult both sides by h(x) - but this is a redundant step as you can observe, since you still get f(x)-g(x)=0 \Rightarrow f(x)=g(x)
    Offline

    20
    ReputationRep:
    if you have

    x/5 = w/5

    then you can say

    x = w
 
 
 
Reply
Submit reply
Turn on thread page Beta
Updated: November 1, 2017
Poll
“Yanny” or “Laurel”
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.