angular post request with content-type application/json not working

the HTTP method always removed and all posted data removed from request body

In the screenshot you shared, we can find that the request you captured is a OPTIONS request (preflight request), not actual POST request. So the data you posted is not in request body.

Besides, the following code snippet works well on my side, you can refer to it.

var student = {'name' : 'testuser', 'age' : 29};

const headers = new HttpHeaders().set('Content-Type','application/json');

this.http.post<Student>('https://xxxx/student',JSON.stringify(student),{headers:headers})
.subscribe(data => {
  console.log(data);
});

Controller and Action

[Route("[controller]")]
[ApiController]
public class StudentController : ControllerBase
{
    [HttpPost]
    public IActionResult Post(Student student)
    {
        return Ok(student);
    }
}

Test Result

I just wanted to expand Fei Han answer. If you are using asp core as server side you should configure Cors in Startup.cs like this :

app.UseCors(x =>
    x.AllowAnyHeader()
    .AllowAnyMethod()
    .AllowAnyOrigin());

If you set Accept headers like this, its enough.

 const headers = new HttpHeaders()
      .set('Accept', 'application/json');

No need to set content headers.