Answer
$0$
Work Step by Step
\begin{align*}
\lim _{t\rightarrow 0} \frac{\cos t-\cos^2t}{t } &=\lim _{t\rightarrow 0} \frac{(1-\cos t)\cos t}{t } \\
&=\lim _{t\rightarrow 0} \frac{1-\cos t}{t } \lim _{t\rightarrow 0} \cos t \\
&=0.
\end{align*}
Where we used the fact that $\lim _{t\rightarrow 0} \frac{1-\cos t}{t } =0.$
