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In any triangle A B C , prove that follo...

In any triangle `A B C` , prove that following : `c/(a-b)=(tan(A/2)+tan(B/2))/(tan(A/2)-tan(B/2))`

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`(tan A/2 – tan B/2)/(tan A/2 + tan B/2) = ((sin A/2)/(cos A/2) – (sin B/2)/(cos B/2))/((sin A/2)/(cos A/2) + (sin B/2)/(cos B/2))`

= `(sin A/2 cos B/2 – cos A/2 sin B/2)/(sin A/2 cos B/2 + cos A/2 sin B/2)`

= `sin (A – B)/2/sin (A + B)/2`

(we know `A+ B + C = 180`, so `(A + B)/2 = 90 – C/2, then sin (A + B)/2 = sin (90 – C/2) = cos C/2)`

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