This is certainly possible: Embed Tableau Server. This also is a easier article to follow along with iFrames, and while it references Tableau Public - the mechanics for Tableau Server is exactly the same: Embedding Tableau Public Views in iFrame | Tableau Software
As for secure part of your question, Tableau always authenticates users upon dashboard load. If we don't want our users individually challenged for credentials, you can leverage token based authentication as a SSO: Trusted Authentication. Alternatively if the organization already has other SSO strategies in place, Tableau might integrate directly with those to provide a secure authenticated loading of dashboards even if it is embedded: https://onlinehelp.tableau.com/current/server/en-us/security_auth.htm
Consider the below use case,
I try to create an application like digital signage solution(Display Monkey - Open Source Digital Signage ). I need to show the dashboard on this digital signage application.
In display monkey, they provide support for listing power bi reports (Power BI API · Apiary) and load the embedded URL in iframe(Step 3: Load a report into an IFrame | Microsoft Power BI ).
In Power bi, they send the access token using post message and render the dashboard using access token at the receiver end. So It doesn't require credentials while render the dashboard.
Do you have an option like this?