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.