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Solution 4.2:8

From Förberedande kurs i matematik 1

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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=xy.

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

cos=acosbcos,

where is the only unknown.