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In triangle ABC, prove that the maximum ...

In triangle ABC, prove that the maximum value of `tan(A/2)tan(B/2)tan(C/2)i s R/(2s)`

Text Solution

Verified by Experts

For triangle ABC, we have
`tan.(A)/(2) tan.(B)/(2) tan.(C)/(2)`
`= sqrt(((s -b) (s-c))/(s(s-a))) sqrt(((s-a) (s-c))/(s(s-b))) sqrt(((s-a) (s-b))/(2(s-c)))`
`= sqrt(s (s -a) (s-b) (s-c))/(s^(2))`
`= (Delta)/(s^(2)) = (r)/(s) le (R)/(2s)`
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