I have a webpage that implements a set of tabs each showing different content. The tab clicks do not refresh the page but hide/unhide contents at the client side.
No
You can use JavaScript. Some bots, including Google, will execute the JavaScript for the benefit of SEO (showing the correct title in the SERP).
document.title = "Google will run this JS and show the title in the search results!";
However, this is more complex since you are showing and hiding tabs without refreshing the page or changing the URL. Maybe adding an anchor will help as stated by others. I may need to retract my answer.
Articles showing positive results: http://www.aukseo.co.uk/use-javascript-to-generate-seo-friendly-title-tags-1275/ http://www.ifinity.com.au/2012/10/04/Changing_a_Page_Title_with_Javascript_to_update_a_Google_SERP_Entry
Don't always assume a bot won't execute JavaScript. http://searchengineland.com/tested-googlebot-crawls-javascript-heres-learned-220157 Google and other search engines know that the best results to index are the results that the actual end user will see in their browser, including JavaScript.