Question

prove sinh x + sinh y = 2*sinh((x + y)/2)*cosh((x - y)/2)

this is what i done so far
Let a=(x+y)/2
= 2a
b=(x-y)/2
=2b

2a+2b=x
2a-2b=y

Answer 1

if you do the RHS as

\[\large 2 \left( \dfrac{e^{\frac{x+y}{2}} - e^{-\frac{x+y}{2}}}{2}\right).\left( \dfrac{e^{\frac{x-y}{2}} + e^{-\frac{x-y}{2}}}{2}\right)\]

Answer 2

did that but i stuck halfway, that's why i try to apply the identities

Answer 3

multiply that term by term

Answer 4

well, first term of the expansion would be

\[\large e^{\frac{x+y}{2}}.e^{\frac{x-y}{2}} = e^x\]

it just unfolds

Answer 5

so i got \[2(\frac{ e^x + e^y- e^y-x}{2 })\]

Answer 6

you miss one 2 in denominater

Answer 7

oh yeah i forgot to multiply it

Answer 8

after this i should apply the exponent properties, but how can i can make x and y become negative

Answer 9

e^x + e^y -(e^-x) - (e^-y) upon 2

Answer 10

i see my mistake now, thank you for your helps, i really appreciate it