I want to prove that $\frac{\sin t}{t}$ is concave in $[0,\frac{\pi}{2}]$,but when I differentiate twice, I get
$-\frac{\sin t}{t}-2\frac{\cos t}{t^2}+2\frac{sint}{t^3}$
then simplify it, I want to prove
$-\tan (t)t^2-2t+2tan(t)<0$,but I can't continue,can anyone give a help?