> 
> Pick out the true statements: 
> 
> 
> a. If $P$ is a polynomial in one variable with real coefficients which has all its
>  roots real, then its derivative $P'$ has all its roots real as well. 
> 
> 
> b. The equation $\cos(\sin x) = x$ has exactly one solution in the interval $[0,\pi/2]$.
> 
> 
> c. $\cos x > 1 −x^2/2$ for all $x > 0$. 
> 
> 
> 

My thoughts:

By Rolles theorem, (a) must be true, but I am not sure about the others.