29. yn anyABC, prove that a (b cos C-c cos B)-02-ec cos B) bc

1.	29. yn anyABC, prove that a (b cos C-c cos B)-02-ec cos B) bc
Answer» cosB= a²+c²_b²/ 2ac and , cosC= a²+b²-c²/ 2ab therefore, a(bcosC – c cosB) = a(b(a²+b²-c²/ 2ab) –c( a² +c²_b²/ 2ac) =a[a²+b²-c²/ 2a - a² +c²_b²/ 2a] =a[a²+b²-c²– (a² +c²_b²)] /2a =a^2+b²-c²–a^2–c²+b²/2 =2b² – 2c² / 2 = b²– c² Like my answer if you find it useful!

Answer»

cosB= a²+c²_b²/ 2ac

and , cosC= a²+b²-c²/ 2ab

therefore, a(bcosC – c cosB)

= a(b(a²+b²-c²/ 2ab) –c( a² +c²_b²/ 2ac)

=a[a²+b²-c²/ 2a - a² +c²_b²/ 2a]

=a[a²+b²-c²– (a² +c²_b²)] /2a

=a^2+b²-c²–a^2–c²+b²/2

=2b² – 2c² / 2

= b²– c²

Like my answer if you find it useful!

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