If P1, P2, P3 are altitudes of a triangle ABC from the vertices A, B, C and is the area of the triangle, then P^-1+P^-2+P^-3 is equal to If P1, P2, P3 are altitudes of a triangle ABC from the vertices A, B, C and  is the area of the triangle , then P^-1+P^-2+P^-3  is equal to
Using Area of Triangle in Terms of Side and Altitude formula,

$$\triangle=\frac12a\cdot P_1\implies\frac1{P_1}=\frac a{2\triangle}$$

$$\implies \sum\frac1{P_1}=\frac{a+b+c}{2\triangle}$$

Using Area of Triangle in Terms of Inradius formula, $$\triangle=r\cdot s$$

where $r$ is the inradius  and $2s=a+b+c$
Using Area of triangle in terms of side and altitude formula, 
Triangle= 1/2 a. P1=>1/p1=a/2triangle
        => £1/p1=a+b+c/2triangle

Using Area of triangle in terms of inradius formula,
Triangle= r.s
Where r is inradius and 
2s=a+b+c
Hope it is useful......