Jesus claimed that He was fully God and fully man.  This is made clear in the first chapter of the gospel of John.  Jesus allowed himself to be killed so that the punishment meant for you and me would be transferred to Himself by His death on the cross. Jesus proved He was God by rising from the dead three days later.

The disciples testified through their own deaths that the resurrection was true.  Everyone except John and Judas died a painful death.  Every one of them could have escaped death if they would have testified that the resurrection of Jesus was a hoax.  Think about it, no man would die for something that didn’t happen and under the penalty of death most men would deny the truth.  The martyrdom of the disciples is a very powerful and compelling testimony.