Mathematical proof for engineering (applying compound / double angle formulas)

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The instantaneous current $i$ and the instantaneous voltage $v$ in a pure resistance a.c. circuit is given by:

$$i=i_{\text{max}} \sin \omega t$$ $$ \text{and} \space v= v_{\text{max}} \sin \omega t$$

Since the power follows:

$$P = iv =i^2 R$$

Show that an equation for instantaneous power is;

$$P=i_{\text{max}}^2 R[1-\cos 2(\omega t)]/2$$

I have been revising basic compound angles and I am struggling to understand the following question from the examples I have previously studied on such topic.

I cannot see how the compound angle formulae relates to this question (if I am correct in thinking that it is relevant for a question of this nature).

A first step, or point of direction/suggestion would be brilliant. Thank You.

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If you're question is "how can I turn $(\sin(\omega t))^2$ into a double-angle-type form", then you should look at your double angle formulas.