What is the value of tan 15 degree in fraction?

The value of ( \tan 15^\circ ) can be calculated using the tangent subtraction formula:

[ \tan(15^\circ) = \tan(45^\circ - 30^\circ) = \frac{\tan 45^\circ - \tan 30^\circ}{1 + \tan 45^\circ \tan 30^\circ} ]

Substituting the known values ( \tan 45^\circ = 1 ) and ( \tan 30^\circ = \frac{1}{\sqrt{3}} ), we find:

[ \tan(15^\circ) = \frac{1 - \frac{1}{\sqrt{3}}}{1 + 1 \cdot \frac{1}{\sqrt{3}}} = \frac{\sqrt{3} - 1}{\sqrt{3} + 1} ]

Thus, ( \tan 15^\circ = 2 - \sqrt{3} ) in its simplest fractional form.