Question

hyperbolic sinh(x+y) deriving help

Answer 1

http://imgur.com/4tQfRv1

Answer 2

@ganeshie8 @rolypoly

Answer 3

what happens if you plug in (x+y) to the function. (Hint: you get e to an exponent, which means you can write it as multiplication)

Answer 4

then you can just factor it into separated terms :)

Answer 5

ye i did how to factor into form ?

Answer 6

https://fbcdn-sphotos-h-a.akamaihd.net/hphotos-ak-prn2/v/t34.0-12/10171163_656891167709484_4814408704206338140_n.jpg?oh=b50e805d6a34dd299f63adc5167243eb&oe=534FA25F&__gda__=1397727388_93cd6d0fe40f43e7fb1b1b9a3c75616d

Answer 7

I don't understand your third step. I'll work on it just a sec

Answer 8

i multipled by e^(x+y) to make right term one!

Answer 9

wait i cant do that i think

Answer 10

ah, Gotcha, but you can't just multiply by something without dividing to "pay for it"

Answer 11

yeah my bad forgot ... what to do then ?

Answer 12

hi ????

Answer 13

replace each term of e^x with sinh(x)+cosh(x) (which is proven in and of itself from the equations you gave)
Do the same with e^y to sinh(y)+cosh(y)

Answer 14

make sure to preserve the negatives. Then use properties of odd and even functions to prove it

Answer 15

why don't you apply cosh(x+y) = sinh x sinhy + coshx coshy?

Answer 16

i.e. sinh(-x)=-sinh(x)
cosh(-x)=cos(x)

These are also proven by plugging in -x to the equations given and solving

Answer 17

....he is trying to prove that sum formula lol

Answer 18

ok

Answer 19

did you understand what to do? after that it is just simplification algebra.

Answer 20

e^x with sinh(x)+cosh(x) (which is proven in and of itself from the equations you gave)
how so?

Answer 21

yes

Answer 22

oh right just add the 2 got it

Answer 23

? I have no reference to what you just said :P if have any problems, just show me your work.

Answer 24

are there any other ways to do it ?

Answer 25

uh....if you don't substitute in you can still do it its just really messy. its much nicer if you use the functions to sub in because you want to end up with theres functions

Answer 26

but then how do you know do add sinh(x) and cosh(x) to get identity = e^x ?

Answer 27

the definitions you gave me in the image.

Answer 28

yeah i mean how do you know you need to use that identity b adding them

Answer 29

how do I know to use it? because you want to find sinh(x+y) in terms of sinh(x), sinh(y),........
those four things. So it makes it a LOT easier to use this identity. Idk how I knew, its kind of intuitive. When you want to find it in terms of certain functions you should usually try to find a relationship between those functions and some term in your equation.

Answer 30

thanks i got it !