2 + \sqrt{3}
1 + \sqrt{3}
\sqrt{3} - 1
2 - \sqrt{3}
Correct answer is D
\tan 15 = \tan (60 - 45)
\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}
\tan (60 - 45) = \frac{\tan 60 - \tan 45}{1 + \tan 60 \tan 45}
= \frac{\sqrt{3} - 1}{1 + (\sqrt{3} \times 1)}
= \frac{\sqrt{3} - 1}{1 + \sqrt{3}}
Rationalizing by multiplying denominator and numerator by 1 - \sqrt{3},
\tan 15 = 2 - \sqrt{3}
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