@LuckyChouhan I have given a closer look to the links you've sent me and
mathb.in/79742 is interesting, I know the sin(2x) = 2sin(x)cos(x) it is a basic formula that I remember was introduced way back in high school or even earlier, and I would have think of tinkering with it like it is done in that linked example. Did you come up with it yourself? The second
math.berkeley.edu/~nikhil/courses/185.f15/hammond.pdf link sadly is too hard for me to comprehend.