If x = a − b , y =b − c , z = c −

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If x = a − b , y = b − c , z = c − a , then (1 − x)(1 − y)(1 − z) is equal to
a + b b + c c + a (1 + x)(1 + y)(1 + z)

x	=	a − b
1	=	a + b

By componendo and dividendo,

=	a + b − a + b	=	b
	a + b + a − b		a

Similarly,

1 − y	=	c	;	1 − z	=	a
1 + y	=	b	;	1 + z	=	c

∴ Expression =	(1 − x)(1 − y)(1 − z)
	(1 + x)(1 + y)(1 + z)

=	b	×	c	×	a	= 1
	a		b		c

If x =	a − b	, y =	b − c	, z =	c − a	, then	(1 − x)(1 − y)(1 − z)	is equal to
	a + b		b + c		c + a		(1 + x)(1 + y)(1 + z)