Question: "Use an Addition or Subtraction Formula to write..."

High School
Geometry
Trigonometry
Trigonometric Functions

Eden Serrano

Open question

2022-08-18

Use an Addition or Subtraction Formula to write the expression as a trigonometric function of one number, and then find its exact value.

\frac{\tan \frac{π}{18} + \tan \frac{π}{9}}{1 - \tan \frac{π}{18} \tan \frac{π}{9}}

Answer & Explanation

lywyk0

Beginner2022-08-19Added 12 answers

The formula can be written as the tangent of the product of angles $\frac{π}{18} and \frac{π}{9}$ because according to the Addition formula for Tangents, $\tan (α + β) = \frac{\tan α + \tan β}{1 - \tan α \tan β} w h e r e α = \frac{π}{18} and β = \frac{π}{9}$ .
We remember that
$\tan \frac{π}{6} = \frac{\sqrt{3}}{3}$ .
$\frac{\tan \frac{π}{18} + \tan \frac{π}{9}}{1 - \tan \frac{π}{18} \tan \frac{π}{9}} = \tan (\frac{π}{18} + \frac{π}{9})$
$= \tan \frac{π}{6}$
$= \frac{\sqrt{3}}{3}$
Answer:
$\frac{\sqrt{3}}{3}$

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