- #1
trollcast
Gold Member
- 282
- 13
Homework Statement
Calculate the value of [itex]\tan(\frac{\pi}{12})[/itex] without the use of a calculator and showing all steps.
Homework Equations
Compound angle formula / Double angle formula
The Attempt at a Solution
Using an equilateral triangle of side length 2 I've shown that:
$$\tan(\frac{\pi}{6})=\frac{1}{\sqrt{3}}$$
Then using the double angle formula:
$$\tan(2\theta)=\frac{2\tan(\theta)}{1-\tan^2(\theta)}$$
Substituting the value for [itex]\tan(\frac{\pi}{12})[/itex] in as 2θ and solving for [itex]\tan(\theta)[/itex]:
$$\tan(\frac{\pi}{12})=\pm2-\sqrt(3)$$
However how do I show that I only need to take the positive solution?
Thanks