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If the cotangents of half the angles of ...

If the cotangents of half the angles of a triangle are in A.P., then prove that the sides are in A.P.

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`cot.(A)/(2), cot.(B)/(2), cot.(C)/(2)` are in A.P.
`rArr 2 cot.(B)/(2) = cot.(A)/(2) + cot.(C)/(2)`
`rArr 2 sqrt((s (s -b))/((s-a) (s-c))) = sqrt((s (s -a))/((s -b) (s-c))) + sqrt((s (s-c))/((s - a) (s -b)))`
`rArr 2(s-b) = s-a + s -c`
`rArr 2b = a + c`
`rArr` a, b, c are in A.P.
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