Answer:[tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]Step-by-step explanation:I'm going to write 105 as a sum of numbers on the unit circle.If I do that, I must use the sum identity for sine.[tex]\sin(105)=\sin(60+45)[/tex][tex]\sin(60)\cos(45)+\sin(45)\cos(60)[/tex]Plug in the values for sin(60),cos(45), sin(45),cos(60)[tex]\frac{\sqrt{3}}{2}\frac{\sqrt{2}}{2}+\frac{\sqrt{2}}{2}\frac{1}{2}[/tex][tex]\frac{\sqrt{3}\sqrt{2}+\sqrt{2}}{4}[/tex][tex]\frac{\sqrt{6}+\sqrt{2}}{4}[/tex]