Q. 55.0( 1 Vote )

# For any ΔABC, show that - b (c cos A – a cos C) = c2 – a2

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:

b (c cos A – a cos C) = c2 – a2

As LHS contain bc cos A and ab cos C which can be obtained from cosine formulae.

From cosine formula we have:

Cos A = bc cos A = …..eqn 1

And Cos C = ab cos C = ……eqn 2

Subtracting eqn 2 from eqn 1:

bc cos A - ab cos C = - bc cos A - ab cos C = c2 - a2

b(c cos A - a cos C) = c2 - a2 proved

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