Cosine Formula (Cosine Rule)

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Theorem:

If ABC is a triangle with sides a = BC, b = CA, c = AB, then prove that

In figure (i),

A < 90^o

But from D BAE, we have

In figure (ii),

A > 90^o

But from D BAE, we have

In figure(iii),

From (i), (ii) and (iii), we conclude that

Similarly, b² = c² + a² - 2 ca cos B

Example:

Suggested answer:

Dividing throughout by 2abc, we get