To prove: The relation cosh(sinhx)<sinh(cosh(x)).
Solution: We proved the inequality as shown below.
Formulae used: The hyperbolic property
For any y≥0, notice
There is a little inequality:
By using MVT, it could be found ξ∈(y,1+y2) such that:
Sincee−y=cosh(y)−sinh(y), this will provide:
Substitute y by sinh(x) and notice 1+y2=cosh(x), this reduces to desired inequality and hence,