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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 7: Q. 17 (page 485)

Find the exact value of the expression:
$\tan 15^{鈭�}$

Short Answer

Expert verified

$(\frac{3 鈭� \sqrt{3}}{3 + \sqrt{3}})$

Step by step solution

01

Step 1. Given information

We have been given an expression $\tan 15^{鈭�}$ .

We have to find its exact value.

02

Step 2. Simplify the expression

We can also write the expression as:

$\tan 15^{掳} = \tan (45^{掳} - 30 掳)$

03

Step 3. Apply the compound angle formula

$\tan (45^{掳} - 30 掳)$ has the form $\tan (伪 - 尾)$

Therefore, apply

$\tan (伪 - 尾) = \frac{\tan 伪 - \tan 尾}{1 + \tan 伪 \tan 尾}$

role="math" localid="1646472011032" $\begin{aligned} \frac{\tan (45^{鈭�}) 鈭� \tan (30^{鈭�})}{1 + \tan (45^{鈭�}) \tan (30^{鈭�})} = \frac{1 鈭� (\frac{\sqrt{3}}{3})}{1 + (1 (\frac{\sqrt{3}}{3}))} \\ = \frac{(\frac{3}{3}) 鈭� (\frac{\sqrt{3}}{3})}{(\frac{3}{3}) + (\frac{\sqrt{3}}{3})} \\ = \frac{(\frac{3 鈭� \sqrt{3}}{3})}{(\frac{3 + \sqrt{3}}{3})} \\ = (\frac{3 鈭� \sqrt{3}}{3 + \sqrt{3}}) \end{aligned}$

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Most popular questions from this chapter

solve each equation on the interval

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