Following this article https://www.digitalocean.com/community/tutorials/how-to-set-up-a-remote-database-to-optimize-site-performance-with-mysql

I setup a remote database for My Magento Application. Now facing below issue

I am using ssl certificate for few sections of website like customer account & shopping cart etc, but now the issue is that the browser is not recognizing the ssl certificate and throwing warning, like proceed with own risk, so what I need to do that to avoid SSL errors ? Can I use the same ssl certificate for Remote DB server as well?