Question 9
For how many positive integers $n$ less than or equal to $1000$ is $$
\begin{aligned} &(\sin t + i \cos t)^n \\ &= \sin nt + i \cos nt \end{aligned}
$$ true for all real $t?$
\begin{aligned} &(\sin t + i \cos t)^n \\ &= \sin nt + i \cos nt \end{aligned}
$$ true for all real $t?$