question_answer

The value of \[\mathbf{sin}\,\mathbf{45}{}^\circ .\,\mathbf{cos}\,\mathbf{30}{}^\circ -\mathbf{cos}\,\mathbf{45}{}^\circ .\,\mathbf{sin}\,\mathbf{30}{}^\circ \] is equal to _________

A)  \[\frac{\sqrt{3}+1}{2}\]           

B)       \[\frac{\sqrt{6}-\sqrt{2}}{4}\]

C)  \[\frac{\sqrt{2}}{4}(\sqrt{3}+\sqrt{2})\]             

D)  \[\frac{\sqrt{6}-\sqrt{2}}{2\sqrt{2}}\]

E)  None of these