The Recon's exclusive weapon is the sniper rifle, which is the most powerful long range weapon in Bad Company 2. As already stated, a headshot will kill an enemy and two bodyshots will also be effective. There is no real secret to using the sniper rifle. It requires good aim, which will come with practice.

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Besides the sniper rifle the Recon can also of course use the all kit weapons, although they don't tend to do the Recon much good. The overwhelming issue with using the all kit weapons is that they're all short range, and the Recon isn't really build for short range combat. Shotty Recons do exist and they seem to think they're pretty smug, but my opinion is that they don't
help out their team nearly as much as a Recon with a rifle. A Recon using a sniper rifle and spotting opponents is doing something only the Recon can do. A Recon with a shotgun isn't doing anything that an Assault, Engineer, or Medic couldn't do better.
The mortar strike is one of the Recon's best tools. The mortar strike is a very effective attack which does huge damage to a large area. It is called in by using the Recon's binoculars. The mortar strike is particularly good at two things. One is taking out distracted enemy vehicles. Vehicles can move out of its range before they are completely destroyed, but if they are already engaging your teammates they probably won't react quickly enough to avoid your strike. The second thing mortar strike excels at is pounding enemy positions and structures into oblivion. Consistently calling in mortar strikes on a building will bring it down, killing everyone inside and destroying any M-Com objective as well.
Recons can also use C4 for the same purpose, but I generally don't recommend it as highly simply because a mortar strike can be used at range and C4 can't. C4 is better at setting traps, however. For example, you can lay some C4 by an objective and then hide out nearby. When you see the enemy enter the room you're guarding, you can blow the charges. Be mindful that you don't assist in the destruction of your own structures, however. C4 is also great for laying traps for enemy vehicles. Simply place it on the road when you see a tank approaching, hide, and then blow the C4 when the tank is on top of it.