Chapter 7: Q. 17 (page 485)

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

Short Answer

Expert verified

$(\frac{3 - \sqrt{3}}{3 + \sqrt{3}})$

Step by step solution

Step 1. Given information

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

We have to find its exact value.

Step 2. Simplify the expression

We can also write the expression as:

$\tan 15^{°} = \tan (45^{°} - 30 °)$

Step 3. Apply the compound angle formula

$\tan (45^{°} - 30 °)$ has the form $\tan (α - β)$

Therefore, apply

$\tan (α - β) = \frac{\tan α - \tan β}{1 + \tan α \tan β}$

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

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

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression

Step 3. Apply the compound angle formula

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Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify the expression

Step 3. Apply the compound angle formula

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Most popular questions from this chapter

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