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: 43

Answer

4 + 2$\sqrt 3$ or 2 (2 + $\sqrt 3$)

Work Step by Step

Given expression = $( \tan 45^{\circ} + \tan 60^{\circ})^{2}$ = $ ( 1+ \sqrt 3)^{2}$ ( substituting for exact values of trigonometric functions) = ( 1 + $2\sqrt 3 $ + 3) [ on expanding using identity $(a+b)^{2} = a^{2} + 2ab + b^{2}$] = 4 + 2$\sqrt 3$ or 2 (2 + $\sqrt 3$)
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