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Prove this hyperbolic equation

Lies and Lies

sinh^2(x) - sinh^2(y) = sinh(x+y)sinh(x-y)

Reply 1

1420787

Have you tried expanding both sides and seeing if you can equate them?

Reply 2

Kvothe the Arcane

Original post by Lies and Lies

sinh^2(x) - sinh^2(y) = sinh(x+y)sinh(x-y)

I'd express the right hand exponentially.

Reply 3

Lies and Lies

Original post by Kvothe the Arcane

I'd express the right hand exponentially.

doing the RHS becomes incredibkly complex

Reply 4

RDKGames

Study Forum Helper

Original post by offhegoes

Have you tried expanding both sides and seeing if you can equate them?

You can't do that - he needs go from LHS to RHS as he is proving they are equal.

Original post by Kvothe the Arcane

I'd express the right hand exponentially.

Notice the forum this is posted in lol... Move it to the maths one :tongue:

Reply 5

Lies and Lies

Original post by offhegoes

Have you tried expanding both sides and seeing if you can equate them?

yep doesn't seem to get anywhere

Reply 6

Lies and Lies

Original post by RDKGames

You can't do that - he needs go from LHS to RHS as he is proving they are equal.

Notice the forum this is posted in lol... Move it to the maths one :tongue:

No I can go either way

Reply 7

ghostwalker

Original post by Lies and Lies

yep doesn't seem to get anywhere

Post some working then.

I would expand both sides.

The RHS only really gets messy is you expand

e^{x+y}

e^xe^y

, etc., so don't - just multply the sinhs together in exponential form. Just remember your rules for indices.

Reply 8

Lies and Lies

Original post by ghostwalker

Post some working then.

I would expand both sides.

The RHS only really gets messy is you expand

e^{x+y}

e^xe^y

, etc., so don't - just multply the sinhs together in exponential form. Just remember your rules for indices.

Reply 9

1420787

Original post by RDKGames

You can't do that - he needs go from LHS to RHS as he is proving they are equal.

There is absolutely no requirement to strictly start with one side and end up with the other. It's perfectly valid, and sometimes easier, to develop both sides until they meet.