If `cosx=(2cosy-1)/(2-cosy),` where `x , y in (0,pi)` then `tan(x/2)xxcot(y/2)` is equal to
(a) `sqrt(2)`
(b) `sqrt(3)`
(c) `1/(sqrt(2))`
(d) `1/(sqrt(3))`

Explanation

To solve the problem, we start with the equation given:

\[ \cos x = \frac{2 \cos y - 1}{2 - \cos y} \]

We want to find the value of \( \tan\left(\frac{x}{2}\right) \cdot \cot\left(\frac{y}{2}\right) \).

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