Question

How does (2+ e^(2t) +(-e)^(-2t) )^.5 = e^t+e^-t work?

Answer 1

how does it simplify

Answer 2

Check and see what\[(e^t + e^{-t})^2\] equals and you'll see what is going on here.

Answer 3

(and the equation you've written down isn't quite right, as you'll see)

Answer 4

really? i checked it in wolfram alpha

Answer 5

Multiply out the expression I wrote down

Answer 6

it becomes e^2t + 2e^(-2t) + e^-2t

Answer 7

OH WAIT!

Answer 8

No

Answer 9

\[(e^t + e^{-t})^2 = e^{2t} + 2.e^t.e^{-t} + e^{-2t} = e^{2t} + 2 + e^{-2t}\]

Answer 10

yes?

Answer 11

oh jeez e^0 = 1

Answer 12

thanks man!