If `a^2,b^2,c^2` are in A.P., prove that `cotA ,cotB ,cotC` are in `AdotPdot`

Explanation

`cotA= (cosA)/(sinA)= (b^(2)+c^(2)-a^(2))/(2bcsinA) = (b^(2)+c^(2)-a^(2))/(4Delta)`
Similarly, `cotB = (a^(2)+c^(2)-b^(2))/(4Delta)`
`therefore a^(2),b^(2),c^(2)` are in A.P.
`-2a^(2), -2b^(2), -2c^(2)` are in A.P.
`(a^(2)+b^(2)+c^(2))-2a^(2), (a^(2)+b^(2)+c^(2))-2b^(2), (a^(2)+b^(2)+c^(2))-2c^(2)` are in A.P.
`b^(2)+c^(2)-a^(2), a^(2)+c^(2)-b^(2), a^(2)+b^(2)-c^(2)` are in A.P.
`(b^(2)+c^(2)-a^(2))/(4Delta), (a^(2)+c^(2)-b^(2))/(4Delta) , (a^(2)+b^(2)-c^(2))/(4Delta)` are in A.P.
`cotA, cotB, cotC` are in A.P.