If x - a - b - a - b - y - b - c - b - c - z - c - a - c - a- then the value of 1- x 1- y 1- z -1- x 1- y 1- z is

Here, x=a ba+b Applying componendo and dividendo ⇒1 x1+x= ba Similarly, 1 y1+y= cb and nbsp;1 z1+z= ac ∴(1 x)(1 y)(1 z)(1+x)(1+y)(1+z)= ab× bc× ca=1 nbsp ...

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Byju's Answer

Standard XII

Mathematics

Section Formula

If x = a - b ...

Question

If $x = \frac{a - b}{a + b}, y = \frac{b - c}{b + c}, z = \frac{c - a}{c + a}$ , then the value of $\frac{(1 - x) (1 - y) (1 - z)}{(1 + x) (1 + y) (1 + z)}$ is

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Solution

Here, $x = \frac{a - b}{a + b}$
Applying componendo and dividendo
$\Rightarrow \frac{1 - x}{1 + x} = \frac{b}{a}$
Similarly,
$\frac{1 - y}{1 + y} = \frac{c}{b}$
and $\frac{1 - z}{1 + z} = \frac{a}{c}$

$∴ \frac{(1 - x) (1 - y) (1 - z)}{(1 + x) (1 + y) (1 + z)} = \frac{a}{b} \times \frac{b}{c} \times \frac{c}{a} = 1$

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