What is Osborn's rule?
It is used in hyperbolic functions; it's the rule to change a
normal trig function into hyperbolic trig function.
Example:
cos(x-y) = cosx cosy + sinx siny
Cosh(x-y) = coshx coshy - sinhx sinhy
Whenever you have a multiplication of sin, you write the
hyperbolic version as sinh but change the sign.
also applied when: tanxsinx (sinx)^2 etc...
Hope this helps you