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: 40

Answer

1 + $\frac{\sqrt 3}{2}$ or $ \frac{ 2 + \sqrt 3 }{2}$

Work Step by Step

Given expression = $( \sin 60^{\circ} + \cos 60^{\circ})^{2}$ = $ \sin^{2} 60^{\circ}$ + 2 $ \sin 60^{\circ} \cos 60^{\circ}$ + $ \cos^{2} 60^{\circ}$ [ on expanding using identity $(a+b)^{2} = a^{2} + 2ab + b^{2}$] = $(\frac{\sqrt 3}{2})^{2}$ + 2$ \times \frac{\sqrt 3}{2} \times\frac{1}{2}$ + $ (\frac{1}{2})^{2}$ = $ \frac{3}{4} + \frac{\sqrt 3}{2} + \frac{1}{4}$ = $ \frac{3}{4} + \frac{1}{4} + \frac{\sqrt 3}{2} $ = $ \frac{(3+1)}{4} + \frac{\sqrt 3}{2} $ = $ \frac{4}{4} + \frac{\sqrt 3}{2} $ = 1 +$ \frac{\sqrt 3}{2} $ or $\frac{2 + \sqrt 3}{2}$
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