Prove that in triangle ABC, the median through A divides the angle A into two parts whose cotangents are 2cotA + cotC and 2cotA + cot B and it makes an angle with the side BC whose cotangent is 1/2 (cotB - cotC).

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Please find below the solution to the asked query:

If ADis median, thenmn=111+1cotθ=cotB-cotC2cotθ=cotB-cotCcotθ=cotB-cotC2 Hence ProvedAlso using both equations of m-n rule, we getcotB-cotC=cotα-cotβ....iAlsoα+β=Acotα+β=cotAcotα.cotβ-1cotα+cotβ=cotA....iiSolve i and ii to get desired result.

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