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JEE Advance - Mathematics (2000 - No. 27)

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

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