In triangle `A B C ,` if `cotA ,cotB ,cotC` are in `AdotPdot,` then `a^2,b^2,c^2` are in ____________ progression.

Explanation

As, `cotA,cotB and cotC` are inA.P.

`:. cotB - cotA = cotC - cotB`

`=>sin(A-B)/(sinAsinB) = sin(B-C)/(sinBsinC)`

`=>sin(A-B)sinC = sinAsin(B-C)`

`=>sin(A-B)sin(pi-(A+B)) = sin(pi-(B+C))sin(B-C)`

`=>sin(A-B)sin(A+B) = sin(B+C)sin(B-C)`

`=>sin^2A-sin^2B = sin^2B-sin^2C`

`=>2sin^2B = sin^2A+sin^2C`

...