Trigonometry 7th Edition

Published by Cengage Learning
ISBN 10: 1111826854
ISBN 13: 978-1-11182-685-7

Chapter 2 - Section 2.1 - Definition II: Right Triangle Trigonometry - 2.1 Problem Set: 41

Answer

0

Work Step by Step

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
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