hi again!
how would you solve these functions:
2cosh2x - sinh2x = 2
and prove
thanks
You need some brackets here I think you mean:
One way is if you know the "Hyperbolic Pythagoras's" theorem:
when it follows at once, but that would be to simple, so we must suppose
that you are expected to expand the hyperbolic funtions in terms of
exponentials. So:
,
and:
,
Then:
,
and:
,
So:
,
and the required result follows on multiplying both sides by
RonL
Hello, dadon!
By the way, natural log is , not .
Prove:
Let
From the definition of , we have: .
On the left side, multiply top and bottom by
Then: . . . .
. . . .
. .
. . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . .
. . . . . . . . . . . . . . . . . .
Therefore: .