You should keep the cough drop whole. This maintains the largest surface-to-volume ratio and slows the dissolution of the cough drop.
The action of the drug can be delayed to either reduce adverse effect if the drugs to the body or to enhance its therapeutic purposes.
Because the throat is dry, the therapeutic purposes of the cough drop would only be achieved if it's dissolution is delayed in the mouth.
To do so, the cough drop should be kept whole to maintain the largest surface-to-volume ratio. This would slow the dissolution of the cough drop.
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