Evaluate sin(105∘)\sin(105^\circ)sin(105∘) using the sum identity sin(A+B)=sinAcosB+cosAsinB\sin(A+B) = \sin A \cos B + \cos A \sin Bsin(A+B)=sinAcosB+cosAsinB.
6+24\frac{\sqrt{6} + \sqrt{2}}{4}46+2
6−24\frac{\sqrt{6} - \sqrt{2}}{4}46−2
3+12\frac{\sqrt{3} + 1}{2}23+1
2−64\frac{\sqrt{2} - \sqrt{6}}{4}42−6