Solving Hyperbolic Trigonometric Equations (2)

An equation of the form (1) may have none, one or two solutions, unlike for the equivalent ordinary trigonometric equation which may have many solutions.

We can solve equations of form (1) by substituting and Then multiply though by and we have a quadratic equation in which we solve by the normal method of substitution and factorisation or use of the quadratic formula.

Example: Solve the equation After simplification and collection of like terms this becomes Multiply by to obtain Substitute to obtain This expression factorises to give We set each factor equal to 0 and solve for y, then use the original substitution to solve for Example: Solve the equation After simplification and collection of like terms this becomes Multiply by to obtain Substitute to obtain This expression does not factorise and we must use the quadratic formula, to 3 sf. which has no value so the only solution is
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