If ` 2 cos alpha = x + 1/x , 2 cos beta = y + 1/ y , 2 cos gamma = z + 1/z` then `xyz + 1/(xyz)` =

If ` 2 cos alpha = x + 1/x , 2 cos beta = y + 1/ y , 2 cos gamma = z +

1.	If ` 2 cos alpha = x + 1/x , 2 cos beta = y + 1/ y , 2 cos gamma = z + 1/z` then `xyz + 1/(xyz)` =
Answer» ` 2 cos alpha = x + 1/x ` `2 x cos alpha = x^2 + 1` `x^2 - 2x cos alpha - 1= 0` `x = -((-2cos alpha) +- sqrt(4 cos^2 alpha- 4))/2` `= cos alpha +- i sin alpha` `= e^(i alpha) or e^(-i alpha)` `x = e^(i alpha) or e^(-i alpha)` `y = e^(i beta) or e^(- i beta)` `z = e^( i gamma) or e^(- i gamma)` `xyx = e^(i(+- alpha +- beta +- gamma))` `1/(xyz) = e^(-i(+- alpha +- beta +- gamma))` `xyz + 1/(xyz) = e^(i phi) + e^(- i phi)= 2 Re ( e^(i phi))` `= 2 cos phi ` `= 2 cos ( +- alpha +- beta +- gamma)` option 2 is correct