Question -
Answer -
Let us consider LHS:
c (a cos B – b cos A)
As LHS contain ca cos B and cb cos A which can beobtained from cosine formulae.
From cosine formula we have:
Cos A = (b2 + c2 – a2)/2bc
bc cos A = (b2 + c2 –a2)/2 … (i)
Cos B = (a2 + c2 – b2)/2ac
ac cos B = (a2 + c2 –b2)/2 … (ii)
Now let us subtract equation (ii) from (i) we get,
ac cos B – bc cos A = (a2 + c2 –b2)/2 – (b2 + c2 – a2)/2
= a2 – b2
∴ c (a cos B – b cos A) =a2 – b2
Hence proved.