If p1,\ p2, p3 are the altitudes of a tr...

If `p_1,\ p_2, p_3` are the altitudes of a triangle from the vertices `A , B , C ,\ &\ ` denotes the area of the triangle, prove that `1/(p_1)+1/(p_2)-1/(p_3)=(2a b)/((a+b+c))cos^2C/2`

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