[br][b]Try inputs like:[/b][br][br]sin(2x), sin(3x), sin(4x)[br][br]TrigExpand[sin(2x)][br][br]TrigExpand[sin(3x)][br][br]TrigExpand[sin(4x)][br]
[b]What pattern do you see in how sine is expanded?[/b]
[b]Define a sequence:[/b][br][br]Sequence[TrigExpand[sin(n x)], n, 1, 5][br][br][br][br][br][br]
[b]What if you tried cos(2x), cos(3x)?[/b]