Question

find sinh(x+y) and cosh(x+y) in terms of sinhx, sinhy, coshx, coshy.

Answer 1

Use the definitions of sinh and cosh along with algebraic manipulation. Remember:\[
\sinh x=\frac{e^x-e^{-x}}{2}\\
\cosh x=\frac{e^x+e^{-x}}{2}
\]

Answer 2

i think its supposed to be how sin(a+b) = sinacosb + cosasinb but with hyperbolic functions but i cant figure it out.

Answer 3

Well what do you have so far? Show what work you have done so I can help you along from there.

Answer 4

i dont really have any work, im not even sure if thats exactly what its asking for but i got the question after watching this video
http://www.youtube.com/watch?v=er_tQOBgo-I&feature=related
, at first i tried plugging in the x+y into the e^x and doing some sort of algebra but i wasnt sure what to do. maybe if you look at the video you will understand better.

Answer 5

Yeah, that's what he's asking for. Just plug (x+y) in for x in the formula and then use the rules of exponents to manipulate it into what you're looking for.

Answer 6

So you start with \[
\sinh(x+y)=\frac{e^{x+y}-e^{-(x+y)}}{2}=\frac{e^xe^y-e^{-x}e^{-y}}{2}
\]Right?

Answer 7

yea but then it wants it in terms of sinhx, sinhy, coshx, coshy

Answer 8

Yes, you need to do more algebraic manipulation.

Answer 9

ok ill give it a shot i just wanted to make sure that i was on the right track, ill let you know if i figure it out.