Using a Reduction Formula

I want to prove equation (1). Note that the equation (2) can be proven by the reduction formula for , but I'll just write the formula down since I know it's true.

I want to show that:

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This seems rather difficult, and I'm not entirely sure where to begin. I'm an amateur, so I don't have much experience with proofs like this. I'll write the equation like this:

(1)

Using the following reduction formula:

(2)

I can write the hypothesis for

So now I have:

Factoring the left side:

(3)

All I've managed to do is write the inductive hypothesis. It's really frustrating that I can't proceed. I can't figure out how to connect one side to the other. Wring the next term for n=k+1 doesn't seem to get me anywhere. Can anyone offer some insight? (Headbang)