Which of following inequalities hold in interval 0 to pi/2 
i tried using calculator and i got 1,2,4 correct .But i am not sure about how to prove them 

For C,
I recognize the right side
as the first 3 terms
of the binomial theorem expansion
of
$\sqrt{1+x}$.
If it is squared,
we get
$\begin{array}\\
(1+\frac{x}{2}-\frac{x^2}{8})^2
&=1+\frac{x^2}{4}+\frac{x^4}{64}
+2\frac{x}{2}-2\frac{x^2}{8}-2\frac{x^3}{16}\\
&=1+x-\frac{x^3}{8}+\frac{x^4}{64}\\
&=1+x-\frac{x^3}{8}(1-\frac{x}{8})\\
&< 1+x\\
\end{array}
$
