Prove that 1 - x a - b 1 - a - c x 1 - b - c 1 - b - a x 1 - c - a 1 - c - b - 1

Let>LHS=y then>y=(1/x^(a b)(a c))(1/x^(b c)(b a))(1/x^(c a)(c b)) then y^(a b)(b c)(c a)=x^ (b c)x^ (c a)x^ (a b) =x^ b+c c+a a+b ...

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Prove that ${(\frac{1}{x^{a - b}})}^{\frac{1}{a - c}} {(x^{\frac{1}{b - c}})}^{\frac{1}{b - a}} {(x^{\frac{1}{c - a}})}^{\frac{1}{c - b}} = 1$

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{(\frac{1}{x^{a - b}})}^{\frac{1}{(a - c)}} . {(\frac{1}{x^{b - c}})}^{\frac{1}{(b - a)}} . {(\frac{1}{x^{c - a}})}^{\frac{1}{(c - b)}} =

(b - c) cot \frac{1}{2} A + (c - a) cot \frac{1}{2} B + (a - b) cot \frac{1}{2} C = 0

Question:- (1/x^a-b)^1/(a-c) . (1/x^b-c)^1/(b-a) . (1/x^c-a)^1/(c-b) = ?

A) 0

B) 1

C) (a+b+c)

D) (a-b+c)²

a (\frac{1}{b} + \frac{1}{c}), b (\frac{1}{c} + \frac{1}{a}), c (\frac{1}{a} + \frac{1}{b})

a, b, c

a (\frac{1}{b} + \frac{1}{c}), b (\frac{1}{c} + \frac{1}{a}), c (\frac{1}{a} + \frac{1}{b})

a, b, c

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