The simplest hyperbolic trigonometric equations involve one function only which may be sinh, cosh or tanh. For example:
Slightly more complex equations involve two functions. We may be able to obtain one function from this hence solve the equation.
Divide by
to obtain
then divide by 4 to obtain
We may have a quadratic hyperbolic equation. We may make a substitution to get a normal quadratic, solve and use the original substitution to solve the original quadratic:
To solve
we may substitute
to obtain
This expression factorises to give
We set each factor equal to 0 and solve:
which has no value, so the only solution is
A quadratic hyperbolic equation may take more than one form, some involving the double angle formulae.
Example:
Set each factor equal to zero and solve if possible:
which has no value.
Example:
We use the double angle formula
Put each factor equal to zero:
which has no value.
The only solution is