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

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

A.

2 + \sqrt{3}

B.

1 + \sqrt{3}

C.

\sqrt{3} - 1

D.

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}