Methods of Proving Trigonometric Identities (1 Viewer)

[xXnukerrrXx]

If we are to prove LHS=RHS can we use the method of LHS-RHS=0 thus proving the fact LHS has to be equal to RHS.

 

[SpiralFlex]

No, you cannot move the RHS, but you can manipulate it. It's best to manipulate the LHS first.

 

[slyhunter]

example?

 

[xXnukerrrXx]

what if you put 'consider: LHS-RHS', wouldn't this open the option of allowing you to freely manipulate it?

 

[SpiralFlex]

You CANNOT ever move or cross multiply with RHS ever in proofs. I am certain of this, but will need some confirmation.

 

[Amogh]

SpiralFlex, are you sure about that?
I personally don't see anything wrong with proving LHS - RHS = 0, and so deriving that LHS = RHS IF the wording of the question allows so. For eg. in a prove by 'simplifying' or a 'Hence prove that' question this method wouldn't be appropriate.

 

[slyhunter]

so what's the question that is so epic that it requires a LHS-RHS=0 proof?

 

[xXnukerrrXx]

just wondering, thats all

 

[Drongoski]

You can prove by showing:

1) LHS = RHS

2) RHS = LHS

3) LHS = M and RHS = M

4) LHS - RHS = 0

First 2 if you can, being most direct. Usually you start from a 'larger' expression to derive the 'simpler' one.

If you can do via 3) you can do via 1) or 2); people sometimes resort to 3) because they are not very confident with their manipulation.

 

[xXnukerrrXx]

You can prove by showing:

1) LHS = RHS

2) RHS = LHS

3) LHS = M and RHS = M

4) LHS - RHS = 0

First 2 if you can, being most direct. Usually you start from a 'larger' expression to derive the 'simpler' one.

If you can do via 3) you can do via 1) or 2); people sometimes resort to 3) because tey are not very confident with their manipulation.

oh thanks

 

[slyhunter]

I use 3) so much LOL

 

[xXnukerrrXx]

I use 3) so much LOL

its epic, so you dont have to think as much!

 

[slyhunter]

exactly

 

[SpiralFlex]

SpiralFlex, are you sure about that?
I personally don't see anything wrong with proving LHS - RHS = 0, and so deriving that LHS = RHS IF the wording of the question allows so. For eg. in a prove by 'simplifying' or a 'Hence prove that' question this method wouldn't be appropriate.

Wouldn't doing that be Show that not prove? I shall check with my teachers.

 

[hscishard]

Farly certain you can do it because mathematically you're still proving it. Though it would be easier to use the more traditional approach

 

[khfreakau]

Wouldn't doing that be Show that not prove? I shall check with my teachers.

No, if you show that the identity RHS - LHS = 0, then you've PROVED it = 0. How does that not constitute proving it, given the information you already have?

 

[XTsquared]

By LHS-RHS=0 you've proven LHS = RHS. The words "Show this" and "Prove this" are basically the same thing.

 

[slyhunter]

show and prove don't mean the same thing derp.

 

[XTsquared]

rofl idiet

 

[Deep Blue]

This whole thread seems pretty pointless. Just prove that LHS = RHS like everyone else by manipulating one into the other.