If `a^2, b^2,c^2` are in A.P., then prove that `tanA ,tanB ,tanC` are in H.P.

Explanation

`a^2,b^2,c^2` are in AP

`2b^2=a^2+c^2`

`b^2-a^2=c^2-b^2`

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

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

`sinCsin(B-A)=sinAsin(C-B)`

`sinC(sinBcosA-cosBsinA)=sinA(sinCcosB-cosCsinB)`

`cotA-cotB=cotB-cotC`

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