Calculate in surd form, the value of \(\tan 15°\).

Explanation

\(\tan 15 = \tan (60 - 45)\)

\(\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}\)

\(\tan (60 - 45) = \frac{\tan 60 - \tan 45}{1 + \tan 60 \tan 45}\)

= \(\frac{\sqrt{3} - 1}{1 + (\sqrt{3} \times 1)}\)

= \(\frac{\sqrt{3} - 1}{1 + \sqrt{3}}\)

Rationalizing by multiplying denominator and numerator by \(1 - \sqrt{3}\),

\(\tan 15 = 2 - \sqrt{3}\)