Solving Hyperbolic Trigonometric Equations (1)

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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 byto obtainthen 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 solvewe may substituteto obtain

This expression factorises to giveWe 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

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