Can you please tell me a geometrical method to prove that 0 < |sin(x)| < √2(1-cos(x)) < |x| ?
The inequality it false for x=2. The easiest way to check an inequality before attempting to prove it is to google search the function. I google searched sqrt(2)*(1-cos(x))-abs(x) to check that part of the inequality and found a value for x when it was not less than zero.
Also, this does not belong in the new users forum