I need to show that if you expand $\displaystyle x(t,\varepsilon)=(1-\varepsilon^2)^{-\frac{1}{2}}e^{-\varepsilon t}sin[(1-\varepsilon^2)^{\frac{1}{2}}t]$ as a power series in $\displaystyle \varepsilon$, you get $\displaystyle x(t,\varepsilon)=sint-\varepsilon t sint+O(\varepsilon^2)$

Any help is appreciated. Thanks!