Let $x = \sin10^\circ$. The formula for $\sin3\theta$ shows that $3x - 4x^3 = \sin30^\circ = \frac12.$ So $8x^3 - 6x + 1 = 0.$ If $y=2x$ then $y^3 -...
No the link was meant to be HTTPS. I was thinking that you might have the HTTP site bookmarked and could be posting through that somehow but honestly...
Well, I don't know about rigorous, but intuitively if you're talking about the limit as $h\to 0$, then $h\not=0$, which forces $\|h\|\not=0$ (in most...
Another way to do this is to use the formula $\sin\frac{\pi}{m}\sin\frac{2\pi}{m}\sin\frac{3\pi}{m}\cdots\,\sin\frac{(m-1)\pi}{m}=\frac{m}{2^{m-1}}$...
I'm just not understanding your question clearly so it's hard for me to try to comment. I know you've spent time explaining but let's start from the...