JEE Advance - Mathematics (2000 - No. 27)

In a triangle $$ABC$$, $$2ac\,\sin {1 \over 2}\left( {A - B + C} \right) = $$

$${a^2} + {b^2} - {c^2}$$

$${c^2} + {a^2} - {b^2}$$

$${b^2} - {c^2} - {a^2}$$

$${c^2} - {a^2} - {b^2}$$