Make a camera follow the player as the player turns around (rotate

Hi guys, I already can make the player rotate around y- axis by the input of the axis that has been defined on the unity editor. But I want camera also rotating while the player rotates. I already made like below, but the camera not rotating, just the player. Anyone could help me?

using UnityEngine;
using System.Collections;

[RequireComponent(typeof(CharacterController))] // This script requires CharacterController attached to the game object where this script attached into

public class CheckPlayer : MonoBehaviour 
{
    private Vector3 moveDirection = Vector3.zero; // Define and set for the movement of the player is not moving by default

    private float gravity = 20.0f, speed = 5.0f; // Define and set for the gravity, speed of the player

    private void Update()
    {
        // Rotate the Player
        transform.Rotate(0, Input.GetAxis("Rotate") * 60.0f * Time.deltaTime, 0);

        Camera.main.transform.eulerAngles = new Vector3(0, Input.GetAxis("Rotate") * 60.0f * Time.deltaTime, 0);

        // Get the CharacterController component
        CharacterController controller = GetComponent<CharacterController>();

        // If the character is on the ground
        if (controller.isGrounded)
        {
            // Get the axis direction for the movement of the character from the Input in the editor
            moveDirection = new Vector3(Input.GetAxis("Horizontal"), 0, Input.GetAxis("Vertical"));

            // Player movement depends on the move direction
            moveDirection = transform.TransformDirection(moveDirection);

            // The player movement is depends on the player speed
            moveDirection *= speed;
        }

        // How much for the time for player takes to hit the ground because of gravity
        moveDirection.y -= gravity * Time.deltaTime;

        // Move the character each second while pressing the key input defined in the editor
        controller.Move(moveDirection * Time.deltaTime);
    }

    private void OnTriggerEnter(Collider col)
    {
        // If the game object colided with the certain tag
        if (col.gameObject.tag == "Inn's Door")
        {
            // Load another level
            GameManager.LoadLevel("Third Loading Scene");
        }

        // If the game object colided with the certain tag
        else if (col.gameObject.tag == "Field's Door")
        {
            // Load another level
            GameManager.LoadLevel("Fourth Loading Scene");
        }
    }
}

The code above I attached to the player and just refer the camera.

Thank you before

Is there a reason why you couldn’t just attach the camera as a child of your player object? Then you wouldn’t have to use any code at all to move it.