Processing Math: Done

From Förberedande kurs i matematik 1

We start by drawing three auxiliary triangles, and calling the three vertical sides x, y and z, as shown in the figure.

Using the definition of cosine, we can work out x and y from

xy=acos=bcos

and, for the same reason, we know that z satisfies the relation

z=cos.

In addition, we know that the lengths x, y and z satisfy the equality

z=x−y.

If we substitute in the expressions for x, y and z, we obtain the trigonometric equation

cos=acos−bcos,

where is the only unknown.