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If in Delta ABC, tan.(A)/(2) = (5)/(6) a...

If in `Delta ABC, tan.(A)/(2) = (5)/(6) and tan.( C)/(2)= (2)/(5)`, then prove that a, b, and c are in A.P.

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`tan.(A)/(2) = (5)/(6), tan.(C)/(2) = (2)/(5)`
`rArr tan.(A)/(2) tan.(C)/(2) = (s-b)/(s) = (5)/(6) xx (2)/(5) = (1)/(3)`
or `3s - 3b = s`
or `2s = 3b`
or `a + b + c = 3b`
or `a + c = 2b`
Hence, a,b, c are in A.P
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