Algebra 2 (1st Edition)

Published by McDougal Littell

Chapter 14 Trigonometric Graphs, Identities, and Equations - 14.6 Apply Sum and Difference Formulas - 14.6 Exercises - Skill Practice - Page 952: 2

Answer

$2+\sqrt3$

Work Step by Step

I would evaluate $\tan 75^\circ$ by the formula for $\tan(a+b)$ where $a=30^\circ,b=45^\circ$. Then just follow the formula and evaluate the known values. These are: $\tan75^\circ=\frac{\tan30^\circ+\tan45^\circ}{1-\tan30^\circ\tan45^\circ}=\frac{\frac{1}{\sqrt3}+1}{1-\frac{1}{\sqrt3}1}=2+\sqrt3$

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