If in a triangle`A B C ,` `(2cosA)/a+(cos B)/b+(2cosC)/c=a/(b c)+b/(c a)` , then prove that the triangle is right angled.

Explanation

`(2cosA)/a+(cosB)/b +(2cosC)/c = a/(bc)+b/(ca)`

`=>2[cosA/a+cosC/c]+cosB/b = a/(bc)+b/(ca)`

`=>2[(c cosA+ acosC)/(ac)]+cosB/b = a/(bc)+b/(ca)`

From projection formula,

`acosA + c cosA = b`

So, our equation becomes,

`(2b)/(ac)+cosB/b = a/(bc)+b/(ca)`

`=>cosB/b = a/(bc)-b/(ca)`

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