If `sin^(2).(A)/(2), sin^(2).(B)/(2), and sin^(2).(C)/(2)` are in H.P., then prove that the sides of triangle are in H.P

Options

A. A.P.
B. G.P.
C. H.P.
D. none of these

Explanation

It is given that `sin^(2)A/2,sin^(2)B/2,sin^(2)C/2` are in H.P.
`therefore1/(sin^(2)A/2),1/(sin^(2)B/2),1/(sin^(2)C/2)` are in A.P.
`rArr(bc)/((s-b)(s-c)),(ca)/((s-c)(s-a)),(ab)/((s-a)(s-b))` are in A.P.
`rArr(s-a)/a,(s-b)/b,(s-c)/c` are in A.P.
`rArrs/a,s/b,1/c` are in A.P. `rArra,b,c` are in H.P.