In any triangle `A B C` , prove that following: `\ a\ (cosB cos C+cos A)=b(cos C\ cos A+cos B)=c(cos A\ cos B+cos C)dot`

Explanation

`a(\cos B \cdot \cos C+\cos A)`

`a / 2[\cos (B+C)+\cos (B-C)-2 \cos (B+C)]`

`a / 2[\cos (B-C)-\cos (B+C)]`

`a[\sin B \cdot \sin C]`

`k \sin A \cdot \sin B \cdot \sin C`

`b[\sin A \cdot \sin C]`

`b / 2[\cos (A-C)-\cos (A+C)]` Adding and Subtracting `\cos (A+C)`

`b / 2[\cos (A+C)+\cos (A-C)-2 \cos (A+C)]`

`b[\cos A \cdot \cos C-(-\cos B)]`

`b[\cos A \cdot \cos C+\cos B]`


Hence, proved