# For any Δ ABC show that-  Note: In any ΔABC we define ‘a’ as the length of the side opposite to A, ‘b’ as the length of the side opposite to B and ‘c’ as the length of the side opposite to C.

Key point to solve the problem:

Idea of projection Formula:

• c = a cos B + b cos A

• b = c cos A + a cos C

• a = c cos B + b cos C

As we have to prove: We can observe that we can get terms c – b cos A and b – c cos A from projection formula

from projection formula we have-

c = a cos B + b cos A

c – b cos A = a cos B …..eqn 1

Also,

b = c cos A + a cos C

b – c cos A = a cos C ……eqn 2

Dividing eqn 1 by eqn 2, we have-  Hence proved.

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