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$ \tan 15^\circ$ is equivalent to:

1. $2-\sqrt{3}$
2. $5+\sqrt{3}$
3. $\frac{5-\sqrt{3}}{2}$
4. $\frac{5+\sqrt{3}}{2}$

Correct answer: $2-\sqrt{3}$

Solution

Using $\tan(A-B)=\frac{\tan A-\tan B}{1+\tan A\tan B}$ with $A=45^\circ$ and $B=30^\circ$, we get $\tan 15^\circ=2-\sqrt{3}$.

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