I just wanted to clarify this because I have only beaten Crota on Normal mode but I'm getting confident enough to try it on Hard. I was hoping that you don't have to wait till the weekly reset to get Hard mode rewards if you've already beaten it on Normal. That and if you've already beaten it on Hard can you go and beat it again on Normal (if you haven't yet) and get additional Radiant rewards?
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If you do it on hard, you get rewards for normal as well- minus the non primaries from crota