1. ## Simplify Hyperbolic Expressions.

Hey,

I have not been taught simplification of hyperbolics, i understand i may have to use standard integrals such as sinhx = coshx but in reality...

How would we go about simplifying:

$\dfrac{2\sinh\left(a\right)\cosh\left(a\right)}{\ cosh^2\left(a\right)+\sinh^2\left(a\right)}$

2. ## Re: Simplify Hyperbolic Expressions.

hyperbolic identities ... numerator and denominator are both on the list. Once you simplify them, the final simplification is also on the list.

Mathematics reference: Hyperbolic trigonometry identities

3. ## Re: Simplify Hyperbolic Expressions.

thank you for the reference, i will learn this.

4. ## Re: Simplify Hyperbolic Expressions.

So, using the identities...

2sinh(a)cosh(a) = sinh(2a)
cosh^2(a)+sinh^2(a) = cosh(2a)

tanh(x)=sinh(x)/cosh(x) x=2a so