Can I connect HP Ultrium 1760 drive to LSI Logic SAS 3041E controller using the cable on the picture
Solution 1:
Yes - actually both variants would do. SFF-8482 is the standard internal SAS device interface.
I'd prefer the adapter cable since it doesn't introduce additional connections. Watch out for the power connector, so you can connect it to your PSU. The once-ubiquitous Molex plug is getting rare these days.
Of course, the SAS-SATA adapter requires using a standard SATA cable.