Trigonometry (10th Edition)

$\sin$$^{2} 45^{\circ} + \cos$$^{2}$ 45$^{\circ}$ = 1 $\sin$ 45$^{\circ}$ = $\frac{\sqrt2}{2}$ $\cos$ 45$^{\circ}$ = $\frac{\sqrt2}{2}$ $\sin$$^{2} 45^{\circ} = (\frac{\sqrt2}{2})^{2} \sin$$^{2}$ 45$^{\circ}$ = ($\frac{2}{4}$) $\cos$$^{2} 45^{\circ} = (\frac{\sqrt2}{2})^{2} \cos$$^{2}$ 45$^{\circ}$ = ($\frac{2}{4}$) ($\frac{2}{4}$) + ($\frac{2}{4}$) = 1 Thus: 1 = 1 Therefore, $\sin$$^{2} 45^{\circ} + \cos$$^{2}$ 45$^{\circ}$ = 1 is a true statement.