Need Help With This Trigonometry Question

Question

The sum and difference formulas for sine and cosine are not easy to remember. But once you have these down, you can derive the double angle and half angle formulas relatively quickly-- so there's no need to remember these! 

My questions is that How do the double and half angle identities follow from the sum and difference formulas? and Can we reduce the amount we have to remember even further-- say, to just the sum formula?

Answer 1

The double angle formulas all come from the sum formulas for sine and cosine.

The half angle formulas all come from the formula for cos 2x.