How do I prove that [math]\displaystyle\lim_{h\to 0}\frac{\sin (x+h)-\sin (x)}{h}=\cos (x)[/math] and that [math]\displaystyle\lim_{h\to 0}\frac{\cos (x+h)-\cos (x)}{h}=-\sin (x)[/math]?
Does cos x = 0 always imply that sin x = 1?