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If sin^2(A/2), sin^2(B/2), and sin^2(C/...

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.`

Text Solution

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`sin^(2).(A)/(2), sin^(2).(B)/(2), sin^(2).(C)/(2)` are in H.P.
`rArr ((s-b)(s-c))/(bc), ((s-a)(s-c))/(ac),((s-a)(s-b))/(ab)` are in H.P. `rArr (a)/(s-a),(b)/(s-b),(c)/(s-c)` are in H.P
`rArr (s-a)/(a),(s-b)/(b),(s-c)/(c)` are in A.P
`rArr (s)/(a) -1, (s)/(b) -1, (s)/(c) -1` are in A.P
So, a, b and c must be in H.P
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