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

If the cotangents of half the angles of a triangle are in A.P., thenpr

1.	If the cotangents of half the angles of a triangle are in A.P., thenprove that the sides are in A.P.
Answer» `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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If the cotangents of half the angles of a triangle are in A.P., thenprove that the sides are in A.P.

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