Calculate in surd form, the value of \(\tan 15°\).
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Correct Answer: Option D
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 \(1 - \sqrt{3}\),
\(\tan 15 = 2 - \sqrt{3}\)
\(\tan 15 = \tan (60 - 45)\)
\(\tan (x - y) = \frac{\tan x - \tan y}{1 + \tan x \tan y}\)
\(\tan (60 - 45) = \frac{\tan 60 - \tan 45}{1 + \tan 60 \tan 45}\)
= \(\frac{\sqrt{3} - 1}{1 + (\sqrt{3} \times 1)}\)
= \(\frac{\sqrt{3} - 1}{1 + \sqrt{3}}\)
Rationalizing by multiplying denominator and numerator by \(1 - \sqrt{3}\),
\(\tan 15 = 2 - \sqrt{3}\)