angularjs – Navigate by URL not working and not redirecting

I have made a simple angular project using firebase in that project I used angularfire to dealwith sign in and sign out.

I have written an auth service.
The code for auth service is

import { Injectable } from '@angular/core';
import {AngularFireAuth} from "@angular/fire/auth";

    providedIn: 'root'

export class AuthService {

 constructor(private auth: AngularFireAuth) { }

 signUp(email:string , password:string)
   return this.auth.createUserWithEmailAndPassword(email,password);

 signIn(email:string , password:string){
  return this.auth.signInWithEmailAndPassword(email,password);

    return this.auth.authState;

   return this.auth.signOut();


I am dealing with the signout from my header so my header.component.ts file is here

import { AuthService } from './../../services/auth.service';
import { Component, OnInit } from '@angular/core';
import { ToastrService } from "ngx-toastr";
import { Router } from "@angular/router"

  selector: 'app-header',
  templateUrl: './header.component.html',
  styleUrls: ('./header.component.css')
export class HeaderComponent implements OnInit {

   email:string = null;

    private auth:AuthService,
    private router:Router,
     private toastr:ToastrService
  ) { 

      (user) =>{
        console.log(user) //just for checking user 
         if(user) =
        else = null;  


  ngOnInit(): void {
   handleSignOut(){  //hitesh ka code alag h 

         this.toastr.success("Logout Sucessfully") = null;

logout method is working but it is not redirecting me to sign in

if I use then/catch or async/await everything works fine but I am not getting why ?