using differentiation prove that for every x in R on has
cosx>or= 1-(x^2)/2
Let $\displaystyle f(x)=\cos(x)+\frac{x^2}{2}-1$. We have that $\displaystyle f(0)=0$ and $\displaystyle f'(x)=x-\sin(x)$. But if $\displaystyle g(x)=x-\sin(x)$ we see that $\displaystyle g(0)=0$ and $\displaystyle g'(x)=1-\cos(x)\geqslant 0$. Draw your conclusion.