Trigonometry (10th Edition)

$\theta$ = 40$^{\circ}$
$\cos$ $\theta$ = $\sin$ (2$\theta$ - 30$^{\circ}$) According to Cofunction Identities $\cos$ $\theta$ = $\sin$ (2$\theta$ - 30$^{\circ}$) is true only if the sum of the angles is 90$^{\circ}$. Therefore: $\theta$ + (2$\theta$ - 30$^{\circ}$) = 90$^{\circ}$ 3$\theta$ - 30$^{\circ}$ = 90$^{\circ}$ 3$\theta$ = 120$^{\circ}$ $\theta$ = 40$^{\circ}$