Answer
$$\lim_{t\to0}\tan\Big(1-\frac{\sin t}{t}\Big)=0$$
Work Step by Step
$$A=\lim_{t\to0}\tan\Big(1-\frac{\sin t}{t}\Big)$$
$$A=\tan\Big(1-\lim_{t\to0}\frac{\sin t}{t}\Big)$$
Recall that $\lim_{x\to0}\frac{\sin x}{x}=1$ with $x=t$ here.
$$A=\tan(1-1)$$
$$A=\tan0=0$$
