[tex]\displaystyle\bf\\Cos\Big(\frac{3\pi }{2} +\alpha \Big)=\frac{\sqrt{2} }{2} \\\\\\Cos\Big(\frac{3\pi }{2} +\alpha \Big)=Sin\alpha \ \ \ \Rightarrow \ \ \ Sin\alpha =\frac{\sqrt{2} }{2} \\\\\\Cos2\alpha =1-2Sin^{2} \alpha =1-2\cdot\Big(\frac{\sqrt{2} }{2} \Big)^{2} =1-2\cdot \frac{1}{2} =1-1=0\\\\\\Otvet \ : \ Cos2\alpha =0[/tex]