\(\frac{b+c-a}{a}\), \(\frac{c+a-b}{b}\), \(\frac{a+b-c}{c}\) are in A.P.
⇒ \(\frac{b+c-a}{a}\)+ 2, \(\frac{c+a-b}{b}\)+ 2, \(\frac{a+b-c}{c}\)+ 2 are in A.P. (Adding 2 to each term of A.P.)
⇒ \(\frac{b+c+a}{a}\), \(\frac{c+a+b}{b}\), \(\frac{a+b+c}{c}\) are in A.P.
⇒ \(\frac{1}{a}\), \(\frac{1}{b}\),\(\frac{1}{c}\) are in A.P. (Dividing each term by a + b + c)