Trigonometry (10th Edition)

Published by Pearson
ISBN 10: 0321671775
ISBN 13: 978-0-32167-177-6

Chapter 5 - Trigonometric Identities - Section 5.4 Sum and Difference Identities for Sine and Tangent - 5.4 Exercises - Page 222: 74

Answer

$$\tan\theta=\frac{m_2-m_1}{1+m_1m_2}$$

Work Step by Step

From the previous exercise, it has been found that $$\tan\theta=\frac{\tan\beta-\tan\alpha}{1+\tan\alpha\tan\beta}$$ Now we have $m_1$ is the slope of the line that makes an angle of $\alpha$ with $Ox$ and $m_2$ is the slope of the line that makes an angle of $\beta$ with $Ox$. Therefore we can take $\tan\alpha=m_1$ and $\tan\beta=m_2$ and replace back to $\tan\theta$ formula. $$\tan\theta=\frac{m_2-m_1}{1+m_1m_2}$$
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