With most derailleurs, yes, but not with all shifters. The OP rides 10-speed, the cassette you're recommending is 9-speed. Won't work.
There is an IRD cassette 10 spd that covers this range and before the MTB shimano 10 spd came out- this was the one you had to buy if you wanted to climb a wall with 10 spd. BUT IRD cassettes do not change as crisply as Shimano and for that reason-it is better to buy a better quality cassette.
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How long was I in the army? Five foot seven.
Spike Milligan