Lethal Weapon

Los Angeles Police Department (LAPD) Homicide Sergeant Roger Murtaugh (Danny Glover), shortly after his 50th birthday, is partnered with Sergeant Martin Riggs (Mel Gibson), a transfer from the Narcotics division. Riggs is a former U.S. Army Special Forces soldier who lost his wife in a car accident two years prior and has turned suicidal, and has been taking his anger out on suspects, leading to his superiors requesting his transfer. Murtaugh and Riggs quickly find themselves at odds with each other.
Murtaugh is contacted by Michael Hunsaker (Tom Atkins), an old Vietnam War buddy turned banker, but before they can meet, Murtaugh learns that Hunsaker's daughter, Amanda, apparently committed suicide by jumping to her death from her apartment balcony. Autopsy reports show Amanda to have been poisoned with drain cleaner, making the case a possible homicide. Hunsaker tells Murtaugh that he was worried about his daughter's involvement in drugs, prostitution, and hardcore pornography and was trying to get Murtaugh to help her escape that lifestyle.
Murtaugh and Riggs go to see Amanda's pimp, but find a drug lab on the premises, leading to a shootout. Riggs kills the pimp and saves Murtaugh's life, who starts to gain respect for his new partner. Though the case seems closed, Riggs is worried that the only witness to Amanda's apparent suicide was Dixie, another prostitute who was working well outside her normal streets. They go to see her at her home but it explodes as they approach it. Riggs finds parts of a mercury switch from bomb debris, indicating a professional had set the bomb; children that had been nearby witnessed a man approach the house with a Special Forces tattoo similar to Riggs', and Murtaugh suspects Hunsaker knows more than he has let on.
The two approach Hunsaker before Amanda's funeral, where he reveals that he had previously been part of "Shadow Company," a heroin-smuggling operation run by former special forces operators from the Vietnam War, masterminded by retired General Peter McAllister (Mitchell Ryan) and his enigmatic right-hand man, Mr. Joshua (Gary Busey). Hunsaker had been laundering the money but wanted to get out, and when McAllister found out he contacted Murtaugh, he had Amanda killed. As they talk, Joshua arrives in a helicopter and kills Hunsaker. Shadow Company attempts to kill Riggs in a drive-by shooting, but he is saved by a bullet-proof vest. Murtaugh and Riggs fake his death to gain the upper hand.
Shadow Company later kidnaps Murtaugh's daughter Rianne (Traci Wolfe) and demand Murtaugh turn himself over to them for her return. Murtaugh and Riggs plan an ambush at the exchange at El Mirage Lake with Riggs providing sniper support, but Riggs is caught by McAllister and all three are taken to an unknown location. Murtaugh and Riggs are tortured for information, but Riggs manages to overpower his captors, frees Murtaugh and Rianne, and escape to find themselves at a busy nightclub used as a front for Shadow Company. Their cover blown, McAllister and Joshua attempt to flee separately. Joshua manages to get away, but McAllister ends up crashing his car on Hollywood Boulevard and is killed when a box of hand grenades in the car detonates. Murtaugh and Riggs race to Murtaugh's home, knowing Joshua will be after his family. They arrive in time to stop him, and Riggs overpowers him in a fist fight on the front lawn. As officers arrive to take Joshua away, he breaks his bonds and grabs for a gun, but both Murtaugh and Riggs quickly pull their guns and shoot him dead.
After visiting his wife's grave, Riggs spends Christmas with the Murtaughs, having become close friends with Murtaugh and bonding with the rest of the family. Riggs also gives Murtaugh a symbolic gift: an unfired hollow-point bullet which he had been saving to commit suicide, as he does not need it anymore.

Question: What makes Murtaugh start to respect Riggs?
Answer: Riggs saves his life