Hello everybody. Could you explain how the sine equation expands? Thank you.

 

Hello everybody. Could you explain how the sine equation expands? Thank you.
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The signals with the "hat" above them are very small perturbations on top of a "larger" operating point signal.
There is a trigonometric identity, you should be familiar with, for expanding the sin(A+B). Look it up for the proof.
Lastly terms that do not significantly affect the result can be shown to approach either 1 or or the value of the argument and can be replaced by the respective values.
Since this is Homework Help, and not Homework Done For You; you need to show us some of your own work.