Display tab title as ‘blog tagline | blog title’

Yes, you can include a check for is_home() or is_front_page() and return a different title based on that.

Update: TwentyEleven does it like this for example (lines 27 to 45).

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)