Simplifying a arc length problem

[hutchwilco]

Simplifying an arc length problem

I have L= Int(-2..2) sqrt(16*cosh(4*t)^2+9*sinh(4*t)^2+9)

and can use Maple to simplify this to sqrt(25*cosh(4*t)^2)
but I just can't see how that is done. (or how to get maple to show me the steps!)

Can anyone help by showing the steps, including any trig substitutions/identities used?

 

[Peeter]

try the definition of cosh and sinh in terms of exponentials (or use that to derive the hyperbolic equivalent of sin^2 + cos^2 = 1)

 

[Gib Z]

$$1+ \sinh^2 x = ...$$ so $$9 + 9 \sinh^2 (4t) = .....$$?

 

[hutchwilco]

ah! thanks - i can't believe I didn't see that - it's only one step! I often have problems seeing the stripped down identities and applying them to problems which have other factors (eg 9 and 4t etc).
Thanks for the hint