Nitric acid is added to the sodium extract to decompose the cyanide or sulphide of sodium formed during Lassaigne’s test.

If nitrogen or sulphur is present in the organic compound, the sodium fusion extract contains sodium cyanide ($\text{NaCN}$) and sodium sulphide ($\text{Na}_2\text{S}$). These ions would otherwise interfere with the silver nitrate test for halogens by forming their own precipitates.

Therefore, boiling the extract with concentrated nitric acid removes these interfering ions, allowing for the accurate detection of halogens as silver halides ($\text{AgX}$).