Trigonometry (10th Edition)

$\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\sin$(30$^{\circ}$ + 60$^{\circ}$) $\sin$ 30$^{\circ}$ = $\frac{1}{2}$ $\sin$ 60$^{\circ}$ = $\frac{\sqrt3}{2}$ $\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\frac{1}{2}$ + $\frac{\sqrt3}{2}$ $\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\frac{1 + \sqrt3}{2}$ $\sin$(30$^{\circ}$ + 60$^{\circ}$) = $\sin$ 90$^{\circ}$ $\sin$ 90$^{\circ}$ = 1 Thus: $\frac{1 + \sqrt3}{2}$ $\ne$ 1 Therefore, $\sin$ 30$^{\circ}$ + $\sin$ 60$^{\circ}$ = $\sin$(30$^{\circ}$ + 60$^{\circ}$) is a false statement.