Q. 75.0( 1 Vote )

# For any Δ ABC show that-2 (bc cos A + ca cos B + ab cos C) = a2 + b2 + c2l

Note: In any ΔABC we define ‘a’ as length of side opposite to A , ‘b’ as length of side opposite to B and ‘c’ as length of side opposite to C .

Key point to solve the problem:

Idea of cosine formula in ΔABC

Cos A =

Cos B =

Cos C =

As we have to prove:

2 (bc cos A + ca cos B + ab cos C) = a2 + b2 + c2

As LHS contain 2ca cos B, 2ab cos C and 2cb cos A ,which can be obtained from cosine formulae.

From cosine formula we have:

Cos A =

2bc cos A = …..eqn 1

Cos C =

2ab cos C = …eqn 2

And, Cos B =

2ac cos B = ……eqn 3

2bc cos A + 2ab cos C + 2ac cos B = +

2bc cos A + 2ab cos C + 2ac cos B =

2(bc cos A + ab cos C + ac cos B) = proved

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