[tex]sin\left(\frac{9\pi}{4}\right)tan\left(\frac{7\pi}{3}\right)=sin\left(2\frac{1}{4}\pi\right)tan\left(2\frac{1}{3}\pi\right)=sin\left(2\pi+\frac{1}{4}\pi\right)tan\left(2\pi+\frac{1}{3}\pi\right)\\\\=sin\frac{1}{4}\pi tan\frac{1}{3}\pi=\frac{\sqrt2}{2}\cdot\sqrt3=\frac{\sqrt6}{2}[/tex]