## Trigonometry 7th Edition

Given expression = $\sin^{2} 45^{\circ}$ - 2 $\sin 45^{\circ} \cos 45^{\circ}$ + $\cos^{2} 45^{\circ}$ = $(\frac{1}{\sqrt 2})^{2}$ - (2$\times \frac{1}{\sqrt 2} \times\frac{1}{\sqrt 2})$ + $(\frac{1}{\sqrt 2})^{2}$ ( substituting for exact values of trigonometric functions) =$\frac{1}{2} - (2\times \frac{1}{2}) + \frac{1}{2}$ = $\frac{1}{2} + \frac{1}{2} - (2\times \frac{1}{2})$ = 1 - 1 = 0