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In ABC, let a, b and c be the lengths of sides opposite to the angles A, B and C respectively.

Draw a perpendicular from vertex A onto side BC. And call it AM.

Let BM = x, so that MC = a-x.

In ABM and ACM we can write using Pythagorus's theorem,

AM² = c²-x²

AM² = b²-(a-x)²

So that,

c² - x² = b² - (a - x)²

c² - x² = b² - a² +2ax -x²

c² = b² - a² +2ax

x = (c² - b² + a²)/2a

cosB = x/c

= (c² - b² + a²)/2ac

= (a² + c² - b² )/2ac

Similarly we can write the expression for cosA and cosC.

It's called cosine rule.

Regards,

Team,

TopperLearning.