working on part of an expression

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I came across a complicated expression containing cos(4t). I wanted to change it to 1-sin(2t)^2. The tools are trig_reduce, trig_expand, and trig_simplify. One of them expresses everything in trig functions of t and the other two are useless. And all three will work on the entire expression, not just on one part. So this is a very general question: how can I get sage to do something to just one part of an expression, rather than the whole expression? (I suppose I could extract the part, work on it, and then substitute the result back in, but that would be difficult!)

And even on a standalone basis, I don't know how to change cos(4t) to 1-sin(2t)^2.