kill(all)$

load(ntrig)$ load(atrig1)$

van=facebook.com/LearningCalculus$

f(x):=''(fullratsimp(sqrt(1-x^2) - x - sqrt(2)*(1-2*x^2)));

f(3/4);

newton(t):=float(subst(t,x,x-f(x)/diff(f(x),x)))$

newton(1/sqrt(2));

f(1/sqrt(2));

f(-1/4);

newton(newton(-0.2588190451025209));

a:-cos(5*%pi/12);

trigreduce(f(a));

float(%);

      
      van=facebook.com/LearningCalculus$

      Prove:

trigreduce(f(a)) = 0;