question_answer

If \[\text{sin}\left( \text{C}+\text{D} \right)=\text{sinC}.\text{cosD}+\text{cosC}.\text{cosD}\]then the value of sin \[75{}^\circ \] is

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

B)  \[\frac{1}{2}(\sqrt{3}-1)\]

C)  \[\frac{\sqrt{3}}{2}\]                    

D)         \[\frac{1}{2}\]