`sinh^2(x) = (-1+cosh(2x))/2` Verify the identity.

`sinh^2(x) = (-1+cosh(2x))/2`

proof:

LHS=>

`sinh^2(x) =(( e^x - e^(-x))/2)^2 `

= `((e^x - e^(-x))^2)/4`

= `((e^x)^2 - 2e^x e^(-x) + (e^-x)^2)/4`

= `(e^(2x) + e^(-2x )- 2)/4`

 =` (-2 + e^(2x) + e^(-2x))/4 `

 = `((-2 + e^(2x) + e^(-2x))/2)/2`

= `(-1 + (e^(2x) + e^(-2x))/2)/2 `

= `(-1 + cosh 2x)/2 `

= RHS

as LHS=RHS

so,

`sinh^2(x) = (-1+cosh(2x))/2`