Just registered with this excellent-looking site. Hoping to be able to help others with their problems as well as receiving help myself with some trickier problems!
I'm going to start off with a puzzle that I have been asked recently...
Show that sin^2(x) = 1 - cos^2(x)
I understand that this is a half-angle formula, and know how to prove it using rearrangements of the double angle formulas/compound angles. However, I am unsure how to show that the LHS = RHS using the basic trigonometric identities, especially cos^2(x) + sin^2(x) = 1.
Thanks to all in advance.