Question

$a(\cos B\cos C+\cos A)$
$=b(\cos C\cos A+\cos B)$
$=c(\cos A\cos B+\cos C).$

Answer 1

$a(\cos B\cos C+\cos A)$
$=a\{\cos B\cos C-\cos (B+C)\}$
$=a\{\cos B\cos C-\cos B\cos C+\sin B\sin C\}$
Similarly $b(\cos C\cos A+\cos B)$
$=c(\cos A\cos B+\cos C)$
$=k\sin { A } \sin { B } \si$a(\cos B\cos C+\cos A)$

$=a\{\cos B\cos C-\cos (B+C)\}$

$=a\{\cos B\cos C-\cos B\cos C+\sin B\sin C\}$

Similarly $b(\cos C\cos A+\cos B)$

$=c(\cos A\cos B+\cos C)$

$=k\sin A\sin B\sin C$$a(\cos B\cos C+\cos A)$

$=a\{\cos B\cos C-\cos (B+C)\}$

$=a\{\cos B\cos C-\cos B\cos C+\sin B\sin C\}$

Similarly $b(\cos C\cos A+\cos B)$

$=c(\cos A\cos B+\cos C)$

$k=sinAsinBsinCnC$