In the Ramayana, why did Lord Rama kill Vali from behind a tree?

Lord Rama's killing of Vali is elaborately discussed in Valmiki's Ramayana and has been analysed by many great spiritual teachers.

 Due to a misunderstanding between Vali and Sugriva, the two inseparable brothers, the older and stronger Vali had driven Sugriva from their kingdom and was constantly seeking to eliminate him forever. Sugriva had to live in fear until Lord Rama, who was sent into exile, arrived and promised to help Sugriva restore peace in his life, which could only happen when Vali was killed as all efforts for a reconciliation had failed. As per the Lord's arrangement, Sugriva challenged Vali to a combat, but he was defeated and barely managed to escape with his life. On the urging of the Lord, Sugriva challenged his brother again. When the fight was in progress, Lord Rama hid behind a tree and shot an arrow that struck Vali, who immediately collapsed to the ground. He was furious as he had been shot at in a cowardly manner, and he questioned Lord Rama about the religious principles guiding the codes of battle.

This one act does seem to be a stain on the otherwise spotless and virtuous character of Lord Rama, but the Ramayana offers a simple explanation behind the Lord's act.

After being hit, Vali falls to the ground in pain and looks around. He sees Lord Rama approaching him with a smile on His face. In a fit of were a virtuous rage person. and agony How could Vali you says, 'I thought you have done something so vicious? I think it is because of your association with this terrible person Sugriva that you have also become spoiled.'

Lord Rama smiles and He says, 'O Vali, it seems that with the deterioration of the body even the intelligence deteriorates. You are accusing me of immorality without understanding the intricacies of dharma.' Lord Rama further says, 'I am the servant of Bharata who is the ruler of the world. So as a member of the royal order and a servant of the king, it is my duty to protect the virtuous and to punish the unrighteous or the vicious. You, O monkey, have for no reason whatsoever grievously wronged your faithful younger brother Sugriva. Although there was no fault of his, you attacked, insulted, exiled and threatened to take his If that was not enough, you even took up very life. his wife as your wife. And because of all this, you are an aggressor.'

The Vedic scriptures describe six types of and even if they are killed by those who are meant to be upholders of the law, there is no sin incurred. They are: aggressors, one who kidnaps another's wife, administers poison, attacks with deadly weapons, sets fire to the house, steals property or steals wealth. When a policeman arrests a criminal, he is not punished by the law for doing so. The kshatriyas are like the policeman and the aggressors are like the criminals. Since Vali grievously wronged his brother for no good reason, it was Lord Rama's duty to kill him and to give justice to Sugriva. Thus, Vali was killed and the means were justified.

And then the Lord says, 'You are a monkey, and as a hunter, I can kill an animal without necessarily confronting it, while being in a tree or being concealed in the bushes. The kshatriya codes allow one to do that. That is why I have killed you and I have done nothing wrong."

Finally, Lord Rama says, 'O Vali, if you still feel that I have wronged you, then I can give you back your life right now.' 

But upon hearing what Lord Rama had said, Vali accepted his sins and hung his head in shame. He even admitted that he himself had often felt that he had wronged Sugriva, but his ego had not allowed him to apologize. He expressed his happiness that he was leaving his body in the Lord's presence. He left, but not before reconciling with Sugriva and expressing his regret over what he had done. 

Vali's source of power had been a special necklace. As long as he was wearing it, he could not die. That was how he was able to stay alive even after being pierced by Lord Rama's arrow, and that was how he could talk with him for so long. Vali took that necklace and gave it not to his own son, but to Sugriva. It would have been natural for him to give it to his son; nobody would have blamed him for doing so because the necklace would have made his son invincible. But Vali was so transformed by Lord Rama's answer that he realized he had wronged Sugriva and to seek forgiveness, he gave his brother the necklace. Before giving it, he told Angada, his son, 'Don't bear any animosity towards Sugriva or Lord Rama because they have not killed me. It is my own bad deeds that have caused my death. Please serve Sugriva as you have served me and please serve Lord Rama as the Supreme Lord." 

Another question still remains. Why did Lord Rama have to kill Vali stealthily and not directly in battle?

Vali had earlier performed tapasya and in return had received blessings from the celestial gods. He had wanted immortality, but the gods could not grant it to him as they themselves were not immortal. So he asked for immortality in an indirect way by asking for half of his opponents' powers whenever they fought him. Through this clever trick, Vali ensured his victory always. Lord Rama is the Supreme Lord, and He could still have killed Vali: but he honoured anyway, the benedictions of the devatas which stated that anyone who came in front of Vali would lose half of his powers to Vali and thus Vali could never be defeated. The Lord was playing the part of a human being and thus He acted as if He too would have been affected by this benediction.